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This is to certify that the

thesis entitled
ANALOG DESIGN FOR A HEART AND BREATH

RATE MONITOR, WITH APPLICATIONS TO

THE PROCESSING OF BREATH SIGNALS
presented by

ANNE MILLER PHILLIPS

has been accepted towards fulfillment
of the requirements for

 

 

 

M S . degree in W Ewaxugeiwlr

 

Major professor

Date M4; ’>]_ I990

0-7639 MS U is an Aflirnum'vc Action/Equal Opportunity Institution

 

 

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;v

ANALOG DESIGN
FOR A MICROWAVE HEART AND BREATH RATE MONITOR.
\VITH APPLICATIONS TO THE PROCESSING OF BREATH SIGNALS

By

Anne Miller Phillips

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Electrical Engineering and Systems Science

1990

ABSTRACT

ANALOG DESIGN
FOR A MICROWAVE HEART AND BREATH RATE MONITOR.
WITH APPLICATIONS TO THE PROCESSING OF BREATH SIGNALS

By

Anne Miller Phillips

A heart rate monitor, using a microwave detection system. has
been expanded to also monitor the respiratory rate. This report
addresses the design of the monitor's filtering system that
preprocesses both an analog heart and a breath signal (the analog
board). and then investigates various algorithmic methods for
processing the digitized respiratory signal.

Chapter One summarizes the monitor's history. Chapter Two
specifies the analog board design, including: the role of a logarithmic
amplifier in increasing the monitor's dynamic range, the additional
flexibility provided by switched capacitor filters (SCFs), the various
amplification stages, the monitor power system and the external
switch used to select either heart or breath rate processing. The
monitoring device has been implemented, and has been used to
collect both heart and breath signal data.

Chapter Three then summarizes algorithmic methods for
calculating respiratory rates, including: integration, auto-correlation,
power spectrum analysis and recursive maximum likelihood (RML)

estimation.

DEDICATION

To my husband Rod. For all your help and love.

ACKNOWLEDGEMENTS

I would like to thank Dr. Marvin Siegel for the chance to work
on this project and for his suggestions concerning my thesis. Also, I
would like to thank Greg D. Hoshal for all of his help.

This thesis resulted from research that was sponsored by a grant

from the Naval RMD Command, contract number NOOO-82-C-O454.

iv

LIST OF TABLES

TABLE OF CONTENTS

LIST OF FIGURES

Chapter 1
Section 1.1
Section 1.2
Section 1.2-1
Section 1.2-2

Chapter 2
Section 2.1
Section 2.1-1
Section 2.1-2
Section 2.2
Section 2.2-1
Section 2.2—2
Section 2.2-3
Section 2.2-4
Section 2.3
Section 2.3-1
Section 2.3-2
Section 2.3-3

Introduction
The Monitor Overview
The Analog Board Signals
The Input Signal
The Output Signal

The Analog Board Design
Dynamic Range
The Logarithmic Amplifier
The Log Amp Design
Filtering
Switched Capacitor Filters
The Lowpass SCF Design
The Highpass SCF Design
The SCF System
Amplification Stages
First Stage
Second Stage
Level Shift Stage

V

viii

~03me

14
15
15
18
23
24
27
29
33
35
37
42
46

Section 2.4

Section 2.4-1
Section 2.4-2
Section 2.4-3

Chapter 3

Section 3.1
Section 3.2
Section 3.3
Section 3.4

Chapter 4
Section 4.1
Section 4.2

APPENDICES
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
APPENDIX E

vi

Design Results
The Analog Board Design
The Power System
Analog Output Signals

Processing the Breath Signal
Integration
Auto-correlation
Power Spectrum Analysis
Recursive Maximum Likelihood Estimation

Conclusions
Conclusions: Analog Design

Conclusions: Respiratory Processing

Logarithmic Amplifier

Switched Capacitor Filters

Trimming

Sampling Constraints

A Recursive Maximum Likelihood Program

LIST OF REFERENCES

81
86
94
104
109

114
114
117

120
123
132
135
138

144

Table

1

Table 2
Table 3
Table 4
Table 5
Table 6

Table

7

Table 8
Table 9

Table
Table
Table
Table
Table
Table
Table
Table

Table

10
11
12
13
14
15
16
17

18

Table A1

LIST OF TABLES

Bipolar Log Amp's Effect on Dynamic Range
Log's Components

Lowpass Filter Components

Highpass Filter Components

First Stage Components

Second Stage Components

Level Shift Components

Analog Board Resistors

Analog Board Capacitors

Component Devices and Voltage Requirements
Ideal Signal Characteristics

Actual Signal Characteristics

Integrated Signal Characteristics
Auto-correlation Characteristics

Power Spectrum Characteristics

RML Results

Expected Input Ranges Throughout

the Analog Board

Algorithm Breath Rate Summary

Sampling Constraints

vii

62
85
85
93
103
109
113

116
118
137

Figure 1
Figure 2

Figure 3
Figure 4

Figure 5

Figure 7

Figure 8

Figure 9

Figure 1 1
Figure 12
Figure 13
Figure 14
Figure 16
Figure 19
Figure 20
Figure 21
Figure 21'
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 26'

LIST OF FIGURES

The Monitor
The First Part

The Digital Board
Din is Sampled Am“

Analog's Input - Am

Power Spectrum of Am
Generalized Power Spectrum
Amt" Magnitude Beyond Range
A Logarithmic Amplifier

Log Amp Design

Rivet Circuit

Resulting Logarithmic Signal
Parallel Switched Capacitor
The Lowpass SCF

The Highpass SCF

The SCF System

Analog Board's Block Diagram
Linear Amp #1

The First Stage

Linear Amp #2

The Second Stage

Voltage Shifting Amp

Level Shift Results

viii

Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40
Figure 41
Figure 42

Figure 43
Figure 44

Figure 45

Figure 46

Figure 47
Figure 48
Figure 49
Figure 50
Figure 51

ix

The Level Shift

The Analog Board Design
First Part

First Stage

Log Amp

Rivet Circuit

Second Stage

Lowpass SCF

Highpass SCF

Level Shift

Digital Preparation
External Switch

Ribbon Cable Interface
DC/DC Converter (0V, i5V, +12V)
Voltage Converter (-12V)
Voltage Regulator (+8.0V)

Voltage Regulator (+2.5V)
Pulser: Viout (Output of the First Stage)

Pulser: V30“ (Output of the Analog Board)
Heart Signal:

V30ut (Output of the Analog Board)
Absolute Value of the Heart Signal

Power Spectrum of the Heart Signal
Power Spectrum of I Heart I

Breath Signal #1

Breath Signal #2

74

75
76
76
78
79

Figure 52 Breath Signal #3 80
Figure 53 Analog Input (#4) 82
Figure 54 Cosine + Noise (#5) 83
Figure 55 Integrated Breath Signal #1 88
Figure 56 Integrated Breath Signal #2 89
Figure 57 Integrated Breath Signal #3 90
Figure 58 Integrated Analog Input (#4) 91
Figure 59 Integrated Cosine + Noise (#5) 92
Figure 60 Sinusoids: In Phase (13:0) 95
Figure 61 Sinusoids: Out of Phase (15:16) 96
Figure 62 Auto-Correlation of Breath Signal #1 98
Figure 63 Auto-Correlation of Breath Signal #2 99
Figure 64 Auto-Correlation of Breath Signal #3 100
Figure 65 Auto-Correlation of Analog Input (#4) 101
Figure 66 Auto-Correlation of Cosine 4» Noise (#5) 102
Figure 67 Power Spectrum of Breath Signal #1 106
Figure 68 Power Spectrum of Breath Signal #2 106
Figure 69 Power Spectrum of Breath Signal #3 107
Figure 70 Power Spectrum of Analog Input (#4) 107
Figure 71 Power Spectrum of Cosine + Noise (#5) 108
Figure 72 Locations in the Analog Board 1 16
Figure A1 Logarithmic Amplifier 120
Figure A2 Second Order Butterworth Lowpass Filter 123
Figure A3 Second Order SC Butterworth Lowpass Filter 124
Figure A4 Switched Capacitor as a Resistor 1 25

Figure A5 Two-phase Clock 1 26

Figure A6
Figure A7

xi

A Standard Op Amp Filter
A Switched Capacitor Filter

Chapter 1

Introduction

Previous research has shown that human heart rates can be
calculated using an instrument that utilizes low level microwaves
detection [1], [2]. This system has an advantage over other tested
methods of extracting human vital functions (i.e. a stethoscope or
sphygmomanometer), since in microwave detection it is not necessary
that the instrument come in direct contact with the body. In fact.
since microwaves have the ability to penetrate various materials, such
a device may be used in life-saving situations where the detection of a
person's body rates was previously impossible. Some potential
applications of the use of microwave detection of vital functions
include: burn victims where direct contact with the skin could prove
painful and or harmful, military or civilian casualties suited in chemical
or radiation protective clothing, and victims of an avalanche,
earthquake. or underground cave-in.

This thesis deals with two major problems that arise when a
heart rate monitor is modified to include the monitoring of respiratory
rates. The first problem is the design of an analog board that
separates and filters the heart and breath signals. (The analog board's
design is detailed in Chapter Two.) The second problem is the
extraction and processing of the breath signal to determine a
respiratory rate. Four processing methods will be described in
Chapter Three. including: auto-correlation, power spectrum analysis,

1

2

integration and recursive maximum likelihood (RML) estimation.

A portable prototype device for monitoring heart rates (herein
called a monitor) has been built. The general workings of the monitor
described in the remainder of this chapter. The signals involved in
the design of the analog board will also be discussed here.
(Recommendations for future analog board design and breath signal
processing will then be given in Chapter Four.)

Section 1.1
The Monitor Overview

The monitor, as seen in Figure 1, consists of three major
sections connected in series: the first part, the analog board and the
digital board. Each of these three sections performs a particular
function in the device. [The specifies that follow (i.e. 10 GHz
microwave and 64 Kbit EPROM) are aspects of the monitor that had
been determined in a previous design, and will not be detailed in the
discussion presented here.]

The first part of the monitor provides the link between the
human subject and the device, and is further illustrated in Figure 2. It
consists of a patch antenna, a microwave transceiver and a capacitor.
When a DC voltage is applied to the microwave transceiver, a 10.5 GHz
wave is radiated through the patch antenna.

The microwaves, if reflected by an object in their path. are
returned to the transceiver's antenna. Meanwhile, the transceiver
operates as a Doppler radar which utilizes the Doppler effect to
determine the radial component of the relative radar-target velocity

 

Human

 

 

 

I First Part |——D| Analog Board HDigital Board I

[ L.E.D. Rate Display |

 

 

 

 

 

Figure 1. The Monitor

 

Patch Antenna

 
 
 
 

dc drop

  

Doppler

 
   
 

Microwave
Transceiver I'—°"
(10.5 GI'IZ) + V - Font

 
 

*wl

 
 
 

velocity (of chest)

  

 

 

 

Figure 2. The First Part

 

 

 

 

 

 

'I'l‘L clock ___p .5

64 K m clock ___, fig
ROM m
Voltage Reference,2.5V 4——— 30

Voltage Power Supplies fi—— 3

64 K A/D Input 4— — E
EPROM A/ D Input 4— — E
\

Voltage Output — —> is

 

 

 

 

 

 

Figure 3. The Digital Board

[3]. The output from the transceiver consists of a voltage whose
frequency is proportional to the velocity of the object in the beam of
the antenna (i.e. a human chest cavity).

A capacitor, at the transceiver's output. removes the large dc

bias present in the transceiver's output signal. The signal at the
capacitor is both the first part output (Font) and the analog board input

(Am)-

The analog board is the second portion of the monitor. This is
the section where the signal is filtered. amplified and otherwise made
ready for processing at the digital board.

The digital board is the final section of the monitor and is shown
in Figure 3. When the digital board is prepared to sample the analog
output signal, it applies a voltage (which acts as a chip select) to the
analog board's sample-and-hold device. The sample-and-hold output
then represents a relatively stable voltage value from which the analog-

5

to-digital (A/D) converter can sample. The A/D converter requires a
2.5 V voltage reference, and its sampling rate is controlled by the

digital board's software.
After the signal is digitized, up to 64 Kbits of its input signal

(Dm) can be stored in the random-access memory (RAM) located on

the digital board. The current processing algorithm, burned into its
64 Kbits of erasable programmable read-only memory (EPROM).
calculates the rate of the heart signal. This heart rate is then
"outputted", in beats per minute (bpm), to a light emitting diode (LED)
readout which is visible on the monitor's outer surface. (Note that the
digital board will have all of its voltages supplied from the analog
board. Also, the digital board design provides an additional A/ D input
and two software controlled TTL clocks which are used in the analog
board's design detailed in Chapter Two.)

In summary, it can be said that by directing the monitor's
antenna toward a human chest. the first part outputs a voltage (Font)
that is related to the velocity of the chest. The analog board filters the
signal (enabling accurate heart rate processing at the digital board)
and the rate is displayed at the monitor's LED readout.

Section 1.2
The Analog Board Signals

The following notation will be used for the remainder of this
chapter. The time-referenced signal at the analog board's input is Am.

the time-referenced signal at the analog's output (just prior to the
sample-and-hold) is Aout and the digital input signal (just past the A/ D

6

converter) is Din , as illustrated in Figure 4.
The analog board's input signal (Am) is received from the front

end of the monitor. Thus, this signal affects the design of the analog
board considerably. Many of the time and frequency characteristics of
Am have been investigated, and are detailed in Section 1.2-l.

The digital board had been designed prior to the design of the

analog board (in a previous instrument). The analog board design's
filter scheme must then produce an output signal (Aunt) that will meet

the requirements of the digital board (as Din is a digitized Acut)° The
output signal (Aout') should possess the signal characteristics of Din,

which are described in Section 1.2-2.

 

 

 

 

 

Figure 4. Dm is Sampled Amt

Section 1.2-l
The Input Signal

When the monitor's antenna is directed toward the chest of a
reclining subject. the analog input signal, A“, is typical of the signal

7

shown in Figure 5 (sampling rate: 64 Hz). In Figure 5, the periodic
impulses due to the subject's heart beating appear to be superimposed
upon a sinusoid-like signal corresponding to breathing.

The magnitude of the voltage at the analog's input ( IAmI) varies

from person-to-person and with the positioning of the device with
respect to a particular subject's chest. lAml has been experimentally
determined to register in a range of 100 (N to 20 mV. (The
constraints on this voltage were determined experimentally, and a
summary of the method used follows. The distance and position of the
antenna were varied with respect to the chests of several subjects. For
each subject, the maximum and minimum analog input signal levels
were recorded-~both with and without the subjects holding their
breath. The absolute maximum and minimum voltage levels form the
constraints on this range.)

Such a large swing in possible voltages is equivalent to a large
dynamic range [4] for the analog board (at Am), calculated in equation

(1) to be 46 dB.

(1) dynamic range at An = 20 logm(20*10'3 V)

- 20 loglo(100‘10'6 V)
-33.98 dB - (-80.0 dB)
46.02 dB

The analog system should amplify the signals of smaller
magnitude (so as to be detected by the monitor) without resulting in
the saturation of signals of larger magnitude. So, if the analog design
accounts for the dynamic range of the analog's input voltage signal,

 

 

 

 

 

 

 

 

 

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200 400

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1500 -
4
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a 1000 -
m
is
g I
g‘ 500 4
0 1 4 . .
0.0 0.5 1.0 1.5 2.0
mequency (Hz)

 

 

 

Figure 7. Power Spectrum of Am

then the monitor will be capable of processing signals of the expected

magnitude levels.
Also, the analog design should filter Am so that the board's

output signal (Aunt) appears as a clear heart or breath sigma].
Familiarity with the power spectrum of Am will help in the analog

filter design.

The power spectrum in Figure 7 is calculated from the analog
data of Figure 5. (Using: 1024 data points, 0 offset points, 1 segment,
0 inserted zeros and a Hanning window. Note: Only the first 50
points are shown here; as points 512-1024 are the same (mirrored)as
points 0-512 and points 50-512 are relatively equal to zero.) This
power spectrum shows a high concentration of power at 0.31 Hz and a

significant amount at 1.31 Hz. These power concentrations

10

correspond to the breath and heart rates of 18.6 respirations per
minute (r.p.m.) and 78.6 beats per minute (b.p.m.), respectively.

Normally, human heart and respiratory rates can be found to
range from 60-80 b.p.m. and 16-18 r.p.m., respectively. [5] And,
depending on the circumstances (i.e. perhaps the subject is sleeping,
exercising or hyperventilating), these rates could register even higher
or lower than normal. Therefore, for this report it will be assumed
that heart rates are restricted to the range of 30-120 b.p.m. (0.5-2.0
Hz), and respiratory rates be restricted to the range of 6-120 r.p.m.
(0.1-2.0 Hz).

A generalized spectrum can be constructed by categorizing the
movements of a reclining body into three types, caused by the
following: the movement of the lungs (breathing), the movement of
the heart, and the movement of anything else (called background
noise). The power spectra of these individual types of movement are
then summed [6], forming the general analog input power spectrum
shaded in Figure 8.

The power spectrum of the analog input sigial typically reveals
three distinct portions--due to the separate influences of the heart,
lung and background movement. The heart movement results in a
spectrum portion that can be described as impulsive and with a power
of lesser magnitude than that which is due to the breathing. The
impulse can occur at frequencies from 0.5-2.0 Hz. The lung
movement, however, result in a spectrum portion whose peak changes
more gradually with frequency and has power of relatively large
magiitude. (This can be expected, as the movement of a subject's

lungs can often be observed while the movement of their heart can not

 

  
  

OfA in

Background
Noise

Power Spectrum

F
0.1 0.5 1.0 1.5 2.0 2.5 3.0 reg-112311”
L—Heart —l
L—Breath ____J

 

 

 

Figure 8. Generalized Power Spectrum

be visually detected.) The mammum point of the pure power

spectrum is expected at frequencies from 0.1-2.0 Hz. Finally, the
background noise produces a spectrum that exists at low power levels,
over random frequencies. (The particular heart rate of 1.25 Hz and
the respiratory rate of 0.4 Hz are just one possibility. Also, the power
spectrum resulting from a heart's movement quite often reveals

harmonics which are not shown in Figure 8.)

Section 1.2-2
The Output Signal

The monitor's A/D converter results in a digital input limited to
the voltage range of 0.0 V to 2.5 V (recall Figure 4). This fact requires

12

an analog board desig'i that can produce an output sigial having

certain characteristics.
The analog board is expected to limit the voltage swing of Aunt to

2.5 Volts. Without this limitation, the sigial would saturate at the A/ D

converter and a clipped digital input sigial would result--as illustrated
in Figure 9 [7]. Also, Aunt must register in the range from 0.0 V to 2.5

V. (A zero level voltage reference of 1.25 V is to be assumed for the

remainder of the thesis.)

 

/ clipped

<—2.5v
g Din —
z: I
S <—— 125V
3) :

C 0V

 

Samples

 

 

 

Figure 9. Anny-Magnitude Beyond Range

In addition, the presence of the A/D converter makes
quantization round-off error a concern for the analog board design [8].
For, if the design produces an Aout of very small magnitude, the A/D
may not be able to distinguish changes in the signal's voltage.
Therefore, for the purpose of this thesis, an acceptable minimum

signal level will be set at 1.30 V (0.05 V relative to the 1.25 V zero volt

13

reference). The analog board must then produce an output signal

whose dynamic range is 5.68 dB, as calculated in equation (2).

(2) dynamic range of Am1t 20 logm ( 2.5 V) - 20 logm ( 1.30 V )

7.96 dB - 2.28 dB
5.68 dB

(Recall, that the dynamic range at the analog's input was calculated, in
equation (1), to be 46.02 dB. This will be further investigated in a following
section.)

Some last general conditions for the output signal requires that Aout be
either a heart or respiratory sigial which is as clean and noise-free as
possible. There must also be some way for the digital board to discern the
type of signal (heart or respiratory) that is present.

Chapter 2
The Analog Board Design

The design of the monitor's analog board will be explained in
this chapter. Here, it is important to be aware of the restrictions that
were placed upon the analog's output sign] in Section 1.2-2. It is also
desired that CMOS (complimentary metal-oxide semiconductor)
technology be used throughout the design due to its low power
consumption [9].

In Section 2.1, a logarithmic amplifier will be introduced as a
non-linear solution for accommodating the analog input's wide
dynamic range. This filter's configuration will vary depending on
whether a heart or a breath sig’ial is being processed. In the case of
processing a heart signal, a rivet circuit will be implemented in the
feedback loop of the log amp.

A method of filtering heart and breath signals is explained in
Section 2.2, where switched capacitor filters are added to the analog
desigi. Then, Section 2.3 looks at the various stages of linear
amplification needed to match and adjust the voltage levels throughout
the analog board.

Lastly, Section 2.4 will specify the analog board's schematic
desigi, discuss the power system for the monitor and comment on
the appearance of the heart and breath sigials at the analog board
output.

14

Section 2.1
Dynamic Range

Equation (1) (in Chapter One) calculated the dynamic range of
the analog board's input to be 46.02 dB, while equation (2) calculated
that the dynamic range of the analog board's output should not exceed
5.68 dB (to avoid saturation). The analog board design must then be
responsible for a dynamic range reduction of at least 40.34 dB (46.02
dB -5.68 dB).

A logarithmic amplifier (log amp) is a non-linear device capable
of solving the dynamic range problem. The usefulness of this device
will be explained in Section 2.1-l, while Section 2.1-2 will specify the
log amp portion of the analog's desigi.

Section 2.1-1
The Logarithmic Amplifier

The analog design includes a log amp, which allows a reduction

in the dynamic range at the analog board's output (A0“) compared to
that at its input (Am)- A log amp is basically an operational amplifier
with a log element in its feedback loop, such as the device shown in

Figure 11 [10].
This log amp relates its output voltage (Vent) to its input voltage

Wm) by the relationship shown in equation (3). [See Appendix A,

equation (A6).]

15

 

 

 

 

 

 

 

 

 

 

 

Figure 1 l. A Logarithmic Amplifier
V
(3) Vout = K[ ln(Io) - 14%)]

(If, Vout « -K and an ideal op amp is used. Here, 10 is the diode‘s

reverse saturation current and K is a constant dependent on the p-n

junction of the diode.)
A positive voltage is required for Vm, as a result of the function

ln(x) being invalid for the negative values of x [l 1]. Yet, a bipolar
voltage is anticipated at the log amp's input (it is expected at the
analog's input). Therefore, a bipolar logarithmic amplifier (the 2910 -
Optical Electronics, Inc.) will be implemented in the analog design.
The result of the bipolar log amp is similar to the combination of

equation (4) and equation (5) (where an ideal op amp is assumed).

1 7
Using, LOG!“ = the input of the bipolar log amp and LOG”,1t = the

output of the bipolar log amp.

(4) Loo,mt - Kl: mun) - m(fl§9l)] , for Looin « -K.
(5) Looout = K[ ln(Io) - ln(l—ID—Si-q-I-fl, for 1.00.m » K.

The bipolar log amp (2910 - O.E.I.) requires an input voltage
whose magiitude is in a range between 3 mV and 3 V. This
requirement is accommodated by a stage of gain (detailed in Section
2.3-1) producing a log amp input signal ranging between 5 mV and 1
V. (When the signal is out of this range it is due to either a physical
error, or noise which will later be filtered by the analog board.)

Table l. Bipolar Log Amp's Effect on Dynamic Range

 

 

 

 

 

 

 

Sigial @ Log In Signal @ Log Out
1 V 0 dB 4—~ -0.364 V - 8.78 dB 4—-
5 mV ~46.02 dB 4- ~ -0.192 V -14.33 dB <—
-5 mV +0.192 V
-1 V 40364 v
Dynamic Range = 46.02 dB Dynamic Range = 5.55 dB

 

 

 

 

Table 1 illustrates the usefulness of the log amp by applying the
log amp's input voltage range to equation (3). (Where this bipolar 10g

l 8
amp specifies that I0 = 1.4 " 103, K = 0.0326; R=1 K52 will also be

used.)

This table reveals that while the dynamic range at the log amp
input is 46.02 dB (0 dB - (-46.02 dB)), the dynamic range at its output
is only 5.55 dB (-8.78 dB - (-14.33 dB)). This value (5.55 dB) is less
than the maximum dynamic range that will be allowed at the digital
board's input (which is 5.68 dB). Thus, the log amp has become a

solution in meeting the monitor's dynamic range requirement.

Section 2.1-2
The Log Amp Design

The design for the bipolar logarithmic amplifier is shown in
Figure 12. This bipolar log amp requires a variable resistor (R6) for
making its offset adjustments, which are typical when using op amps.
However, a rivet circuit will be switched into the log amp's feedback
loop when the accurate offset adjustments are needed for processing
heart sigials (the switch makes a connection between 1A and 2A).

The rivet's design is shown in Figure 13 and implements a
monolithic JFET operational amplifier (LF356H, National
Semiconductor) as indicated in the log amp's specification sheets.
Here, a capacitor (C14) shorts any AC voltage to g'ound. The input to
the op amp is then free to follow the average DC offset of the rivet's
input, while R7 holds the op amp's inverting input at virtual ground.
The rivet's overall effect is to have the log amp's input follow along a
slow moving frequency (the DC drift).

The specific component values used in the desigi of Figure 12

l9

and Figure 13 are listed in Table 2. The capacitors: C6, C7, C10, C1 1,
C12 and C13, are present in the design in order to store charge and
thus control DC drift at the devices (12]. The capacitors: C1 1 and
C13, are electrolytic Capacitors which polarize the power supply's
voltage drift at this circuit [13]. The remaining capacitors and
resistors in the rivet circuit (C5, C14, R7 and R8) and the variable
resistor (R6) have values as suggested in the log amp's specification
sheets.

The log amp's output is the result of the natural logarithm of the
heart and breath signal and low voltage noise. And, as the logarithm of
a low voltage noise translates into a relatively large magnitude, the
result of the device is an output signal which is embedded in high
frequency noise. (The filtering done in the later portions of the
desig'i will remedy this.)

Figure 14 illustrates the log amp's effect on a signal; since it is
the natural logarithm calculated from the voltage magiitude of the
data of Figure 5. (The sign of the original data of Figure 5 was kept.)
Note that this figure has a relative voltage scale that is only
proportional to the voltage magnitude actually occuring at the monitor.
Notice also, that a pattern of heart and respiratory cycles are revealed
here, just as in Figures 5. The difference is that, unlike the original
input data, the logarithmic signal will now be limited to the voltage
range of 3 mV to 3 V.

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L Rivet
3A __‘ Riv CIICUIt Riv
\__g h
9——
m 2“ Figure 13
._12_ 10K to Loci.n Out 1
L0
14 1K to LOG Log
Loc‘fi in Element 4 g":
a! Log Amp
U3 V+,
9) 1 - - 7
R6 < < +12V
C10 C12
C1 1 C 13
-12V

 

 

 

Figure 12. Log Amp Design

21

 

 

 

 

 

 

 

 

 

 

 

O 0
Figure 13. Rivet Circuit
Table 2. Log's Components
I
Cam Malue g Resistor Kale:
(:5 0.1 ur R6 1 kn
cs 0.1 uF R7 1 Mo
(:7 0.1 pF R8 1 M52
014 0.1 11F
C10 0.1 11F
011 15 uF
C12 0.1 IJF
013 15 11F

 

 

 

 

 

22

 

 

 

 

 

 

 

 

 

 

 

 

 

4.0 -
'i H
2.0 -
I
*5
a.
.5
‘3»
a 0.0 -
“a
5 1
-2.0 -
-4-0 . u - I - I . u
0 200 400 600 800
Sample Number (@ 64 Hz)

 

 

 

Figure 14. Resulting Logarithmic Signal

Section 2.2
Filtering

Previously, the design for the heart monitor included several
cascaded standard op amp lowpass and highpass filters. This design
was adequate for many situations, but was inflexible for the following
reasons: it filtered only heart signals, its filters were difficult to tune.
and once designed the monitor's cutoff frequencies became fixed.

The current monitor design uses switched capacitor filters
(SCFs) to overcome the inflexibilities of the old monitor. Heart and
respiratory signals are both processed through the filter system. The
position change of an external switch enables either heart or breath
processing by routing the signal through different filters, and
produces a voltage signal at the digital board informing the software
which algorithm (heart or breath) it should run.

The filtering method for each type of signal will vary. The heart
signal is processed by cascading a lowpass and a highpass filter: this
enables the final output signal to have reduced disturbances caused by
the presence of low frequency respiratory disturbances and both high
and low frequency noise. The respiratory signal is processed by using
only the lowpass filter. The low cutoff frequencies required (less than
0.1 Hz) would be too low for accurate and stable operation of the
highpass filter.

Adjusting the new SCF design is simplified compared to the
tuning of the RC op amp filters. When a filter's cutoff frequency is
decided upon, an RC filter design requires tedious calculations to

determine specific values for R and C [14]: these values are then often

23

24

only approximated. The cutoff frequency of a SCF is attained by the
frequency supplied by a 'ITL clock, which is proportional to the cutoff
frequency.

Therefore, filter cutoff frequencies are easily altered with the
use of SCFs in the monitor's design. When a change in cutoff
frequency is desired, one need only alter the clock frequency in the
software (the 'ITL clock is supplied by the processor at the digital
board) and burn the new program into an EPROM. This is simple
compared to the past alternative where new RC values needed to be
calculated, and the old components were unsoldered and replaced
with the new-valued components.

Section 2.2-1 discusses the general operation of switched
capacitor filters and their usefulness in the monitor's design. The
details of the specific lowpass and highpass switched capacitor filter
designs will then be shown in Section 2.2-2 and Section 2.2-3.
respectively. Then, Section 2.2-4 discusses the SCF system resulting
from cascading these lowpass and highpass SCFs.

Section 2.2-1
Switched Capacitor Filters

The parallel configuration for a switched capacitor (seen in
Figure 16) can be equivalent to a resistor when it is alone in the
circuit [15]. This is proven in Appendix B which also specifies [in
equation (A23)] the relationship between the value of capacitance (C),
the frequency of the clock that controls the two switches (fc) and the

equivalent resistance (R). This relationship is repeated here as

25

equation (6).

1
(6) R=fc—C-

Therefore, the resistance of an SC (and thus the cutoff frequency of an
SCF) varies according to the frequency of the controlling clock. (See
Appendix B for more detail.)

52 >2
+ +
V1 (3 V2

Figure 16. Parallel Switched Capacitor

 

 

 

 

 

The current monitor design uses both lowpass and highpass

Butterwortln switched capacitor filters (SCFs) [16]--which are detailed
in the following two sections. The cutoff frequency (FCutoff) of each

SCF is related to a switch controlling clock frequency (FClock) by the

relationship revealed in equation (7).

Fem
(7) Fouto£r= 100

 

26

As seen from equation (7), the calculations for determining
switched capacitor filter cutoff frequencies are quite simple. If a
cutoff of 1 Hz is needed, the corresponding clock frequency must be
100 times this, or 100 Hz. [Any lack of precision in the clock's
frequency is reduced by one-hundreth in the filter's cutoff frequency;

if a 1 Hz cutoff frequency is desired, and there is a 0.1 Hz error in the
clock's frequency (say, F010“ = 99.9 Hz), then there would only be a

0.001 H2 error in cutoff frequency (Fcutofl = 0.999 Hz).]

'lhe two clocking signals are to be supplied by the digital board's
two Tl‘L, software controlled clocks (see Section 1.1). The TTL
clocks that control the lowpass and highpass filters will be called
Clock A and Clock B, respectively. [This is just one possible scheme
for the clocking signals (i.e. the lowpass also accepts CMOS clocking
and a Schmitt trigger oscillator: the highpass accepts CMOS
clocking). The TI‘L clocks, however, are conveniently available from
the digital board: so, equation (7) can be applied to each SCF and the
RC calculations involved in Schmitt triggers are eliminated.)

The use of SCFs in the design creates a discontinuity at the
frequency of each clock signal. This is a response to the change in
current flow that occurs as the various switches open and close. The
faster the clock, the less noticeable the change in the SCF's
discontinuity; as the capacitor's charge has little time in which to
vary.

The discontinuities are most noticeable when filtering a
respiratory signal. But, the frequencies of the clock are so much
greater than the signal frequency and the change in voltage from

sample-to-sample is so minor (relative to the magiitude of the heart

.27

or breath signal), that the clock's frequency will either be ignored by
the digital board's software or be filtered away by the level shift's
lowpass filtering (see Section 2.3-3).

Section 2.2-2
The Lowpass SCF Design

The configuration of the lowpass SCF uses an MF6CN-100
(National Semiconductor) integrated chip and is shown in Figure 19.
The MF6 is a sixth order switched capacitor Butterworth lowpass
filter, with two independent op amps. The details stated in this
section are those stated in the manufacturer's specification sheets.

The design voltages are i5 V (as :15 V is a common requirement
for the digital board, and is a supply voltage option available to the
MF6). Of the digital board's two 'ITL clocks, Clock A will control the
cutoff frequency of this filter. This requires that the level shift pin (L
Sh) be tied to ground and that the clock's input be the CLK R pin.

The variable resistor, R14, is used to adjust the filter's DC offset
voltage (see Appendix C-Tuning). And the two capacitors, C8 and C9.
are present to provide filtering at the voltage supply inputs. The
values for these components are shown in Table 3 and are those
recommended in the specification sheets for the MF6.

When there is a signal at the MF6 SC filter's input and the 'ITL
clock is connected and operating at a frequency, Fem“ A , then the

lowpass cutoff frequency (FLP ) is calculated from equation (8).

 

 

 

 

 

 

 

 

 

FILTER OUT 3 ' LE,
8,).
ILTER IN ,_
LP h CIK 9
1 1 CLKR MF6 VADJ _
l I U4 7
Clock A 6

 

 

 

 

 

 

 

Figure 19. The Lowpass SCF

Table 3. Lowpass Filter Components

m Kala: ‘ Emerita: Yams
R14 50m cs 0.1m?

C9 0.1 uF

 

 

 

 

29

F
(8) FL? = $00" A—

Recall (Section 1.2-1), that the lowpass filter will be primarily
used to filter away low magnitude noise--when processing a heart
signal, and noise and heart signals--when processing a respiratory
signal. The sixth order filter operates at120 dB/ decade [17], which is
acceptable for distinguishing heart and respiratory signals (as revealed
in the plots of Section 2.4-3).

Section 2.2-3
The Highpass SCF Design

The MFIOCN (National Semiconductor) is an integrated circuit
chip which contains two secondorder universal monolithic dual
switched capacitor filters. The MF10 is capable of functioning as
either an allpass, lowpass, bandpass, or notch filter--of up to fourth
order when the dual filters are cascaded. 'Ihe bandpass filter option
only permits filtering that is symmetric around a center frequency.
Any use for a bandpass filter will be simulated by cascading the lowpass
(MF6CN-100) and the highpass (NIFIO) switched capacitor filters.
(Many of the details concerning the MF10 and used in this section
come directly from the specification sheets for this chip.)

Figure 20 shows the configuration for an MF10 fourth order
highpass filter (mode 3 from the MF10's specification sheets). Unlike
the MF6, the cutoff frequency for the highpass SCF is dependent on

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31

both the controlling clock's frequency and the designed resistor
ratios. To be consistent with the MF6 design, the MFIO will use a TI‘L
clock signal (Clock B) and will be configured using the divide-by-IOO
option. Each of the former features are options available in MFIO
implementation and are obtained through the following details: the L
Sh pin is tied to analog g'ound (0V) and the 50/ 100/ CL pin is tied to
midsupply (0V is also the midsupply for voltage range i5V).

Equation (9) and equation (10) show the relationships between
the ClOCk'S frequency (FClock B) and the cutoff frequencies of the two

second order highpass filters contained in the MFIO (whose
frequencies are Fm,1 and Far-2' respectively).

FClockB .
(9) Fan = 100 R18

FClockB
(1 0) Fm = _100 V—R22.5

Table 4 lists the actual component values used for the design shown in
Figure 20; this table shows that all four resistors possess the same
resistance (10 KO). The simplified relationship for the resulting 4th
order filter (due to cascading the two 2nd order filters) is shown in
equation (1 I).

F
(11) Fm,=%£

Where FHP is the cutoff frequency of the cascaded highpass SCFs.

32

Table 4. Highpass Filter Components

 

Beam yam Cam 11311.15:
R17 10 K9 C18 0.1 uF
R18 10 K52 019 0.1 uF
R19 10 K9
R195 10 K9
R20 10 KO
R21 10 K0
R22 10 K0
R225 10 m

 

 

 

 

The highpass gain for the resulting fourth order filter (Gap ) is

the product of the gains for each of the two second order portions
(Gum and anz. respectively) [18] and can be determined from

equation ( 12).

Where the relationships between ani and (33,2 and the design's

resistor values of Table 4 are shown in equation (13) and equation (14)

(via the MFIO's specification sheets).

 

 

(13) Gm,ll =(- R17

33

 

..,, =<--2—a)=(-:8K“)=-1

8

Applying the previous results to equation (12) yields an overall gain for
this filter of one (or 0 dB). (Recall: only the heart signal will pass
through this highpass filter so that its 0 dB gain will eliminate any
discrepencies that could appear between the signal gain levels of the
heart and respiratory signals.)

Section 2.2-4
The SCF System

The switched capacitor filter system (see Figure 21) consists of
the SCF highpass and lowpass filters, the controlling TI‘L clocks
(Clock A and Clock B) and the external switch used in routing the
analog signal through the various SCFs. Two poles in a quad-pole
double throw switch are represented in this figure (see Section 2.4-1
for detail). Depending on the position of the switch the signal will
enter the SC lowpass filter and a heart or respiratory filtered signal
will exit the SCF system by the center post of pole ZB.

A heart signal is being processed when the switch is in position 1
(connections are made between poles 1B and 2B, and poles 1C and
2C) resulting in a low voltage at pole 2C. When the digital board
samples and checks the input at 2C, the frequencies of the software
controlled 'ITL clocks (Clock A and Clock B) are adjusted for proper
heart filtering at the SCFs. The signal received at 2B is that which had

34

 

 

 

 

 

 

 

 

 

 

 

HP LP
LE Lowpass SCF Highpass SCF
13
RH —t—’[ |_"' ——°
23

e - F > \—->
LP HP SB V3111

1 1 J

 

 

 

 

 

.Clock A Clock B
10

Digital Board H——/ é
ac (Low)

+2.5 V
(High)

 

 

 

 

 

 

Figure 2 1 . 'Ihe SCF System

proceeded through both the lowpass and the highpass filters.
Similarly, a respiratory signal is received at 2B when the switch
is in position 3 (connections are made between poles ZB and SB, and
poles 2C and 3C). The digitals board will first detect a high voltage at
pole 2C, and will output the proper frequency for the 'ITL clocks.
Note that the signal is diverted from the highpass filter when the 2B

to 3B connection is made.

Section 2.3
Amplification Stages

Linear amplification is used in the analog board's design prior to
three sections: the log amp, the switched capacitor filters and the
sample-hold. The amplification stages establish the input signal
voltages to levels required by each of the three sections. Figure 21'
reveals a block diagram of the analog board.

The log amp is to be the first section of the analog design, as its
purpose is to increase the dynamic range and thus reduce saturation
in the remaining amplifiers. It is preceded by the first stage of
amplification whose design is detailed in Secton 2.3-l. The second
stage of amplification is discussed in Section 2.3-2 and is positioned
before the switched capacitor filters. Finally, a level shift
(amplification stage) is needed to shift the analog's signal into the 0-
2.5 V range required at the input to the sample-hold and is designed
in Section 2.3-3.

35

36

 

From Front End

L

1st Stage of

 

 

 

 

 

 

 

 

 

 

Amplification
i 7 Rivet
Logarithmic 1
Amplifier m C rcuit
2nd Stage of
Amplification

 

 

 

 

 

 

 

Level Shifting
Amplifier

l

{ Digital Board

 

 

 

Preparation

$

To the Digital
Board

 

 

 

 

 

 

Figure 21'. Analog Board's Block Diagram

Section 2.3- 1
First Stage

Section 1.2-l has stated that the magnitude of the analog board's
input ( lAml ) exists in the range of 100 (N to 20mV. However, the

specification sheets for the log amp state that the magnitude of its
input voltage ( ILOGmI ) must exist in the range of 3 mV to 3V. So, in

order to boost the voltage levels from the analog's input up to the
voltage levels that are required by the log amp, a first stage of voltage
gain will be positioned prior to the log amp.

A linear inverting amplifier [19] is shown in Figure 22. Applying
Kirchoff‘s Current Law [20] to the inverting input of this circuit and
assuming an ideal operational amplifier [21],

Vlln ' 0 Vlout ' 0

(15) —R'1—'+—R-2——+0A=0A

'lhis gain then relates the amplifier's voltage input (V 1111) and
voltage output (V lout) as in equation (16).
R2
(16) Vlout = 'fi.vlin

For this first stage of gain, Vnn = Am and V1out = LOCI!n . Thus,

equation (17) follows if (-R2/R1) = Cl.

(17) LOGm=GI‘Am

37

38

 

 

 

 

 

R 1
0—’VV\/—~—
+ —I—->
V

lin
"o

 

 

 

 

 

Figure 22. Linear Amp #1

Based on this equation and the limited voltage range required at

the log amp's input, GI must satisfy the inequalities shown in equation
(18) and equation (19). (Recalling, 100 uV s lAml s 20 mV.)

(18) ILOGmISIGll*lAmlslGll‘ZOmVs3V

(19) lLOGmflzflGll ‘IAmIZIGll*100uV23mV

Using the previous two inequalities to solve for lGl | yields equation
(20) and equation (21).

3V
(20) |G115m= 150

3mV
(21) |G1|2W=30

39

Combining the above inequalities and using lGll = I-R2/R1 I,
(22) 30$lGll=l-R2/R1l.<_150

The analog devices' input resistors are 10 K9 throughout its design so
as to obtain uniform current levels in the devices, Therefore, R1 is to

have a resistance of 10 K9 and from equation (22),
(23) 300mg l-R2 l $1.5M!)

For the design, R2 = 500 K!) so that I01 I can now be calculated

using the stated resistor values.

500K!)
(24) lGll = l- R2/R1 l =W= 50 (34.0 dB)

Using the design results of equation (24) along with equation (18) and
equation (19) ensures that ILOGml will exist in the range as calculated

in equation (25) and equation (26).

(25) ILOGmI SIGII *20mV=50*20mV=1V

(28) ILOGmI 2 lGll * 100 uv=50* 100 uV= 5mV

(Notice that this is within the log amp's operating range 3 mV 5
lbOGml s 3 V.)

The input to the first stage operates at very low signal levels and

40

will be greatly amplified--along with any noise that is created in the
device. Therefore, a low-noise op amp (the OP227 - Precision
Monolithics, Inc.) is used to reduce the output signal's noise.

The component values for the first stage are listed in Table 5
and the final design for the first stage is shown in Figure 23. Here, a
variable resistor (R3) is added for trimming the op amp's offset voltage
to zero (see Appendix C-Trimming). A typical output from this first
stage of amplification is similar to that shown in Figure 14; but, the
output voltage level is within a range that is witlnin the log amp's

acceptable range.

.41

Table 5. First Stage Components

 

999.8939: V_a1_eu
ca 0. 1 (LP
C4 0. 1 uF

 

 

Resistor Kaine

R 1
R2
R3
R4

10 KO

500 K!)
50 KO pot.
190 Q

 

 

 

 

 

 

 

 

 

 

 

 

Figure 23. The First Stage

 

 

Section 2.3-2
Second Stage

The magnitude of the input voltage to the MF6-100 is limited to
a range between 0.3 V and 1.25 V. [This range allows for the analog
board to have a maximum voltage swing of 2.5 V (see Section 1.2-2),
and for the MF6-100 to have an input voltage whose magnitude exists
within the range of 0.3 V and 5 V (as required by its specification
sheets).] However, Section 2.1-1 indicated that the voltage magnitude
for the signal at the log amp's output ( ILOGoutl ) exists in the range of
0.192 V to 0.364 V, when the magnitude of its input voltage exists
between 5mV and l V (as designed in Section 2.3-1). A second stage
of voltage gain will then be positioned prior to the SCF system in order
to match the voltage levels from the log amp to those levels required
at the input to the SCF system. .

A linear inverting amplifier, equivalent to that of Figure 22, is
shown in Figure 24. By assuming: an ideal operational amplifier, V2111

= LOGO“, V20ut = LP“, and GZ = - R1 l/R9, then equation (27) is true

for this circuit. [See equation (16).]

(27) LP!n = G2 " LOGout

Based on this equation and the limited voltage range resulting at

the log amp's output, GZ must satisfy the inequalities shown in
equation (28) and equation (29). (Recalling that 0.192 V s lLOGoutl g

0.364 V.)

42

43

 

 

 

 

 

R9
o—vav—o— -
+ —T—>
v

21::
’0

 

 

 

 

 

Figure 24. Linear Amp #2

(28) )meI 5 I02) * ILOGoutl 5 I02) *0.364Vs 1.25v

(29) ILPmI 2 I02) * lLOGoutl 2 )02) *0.192vz0.3v

Using the previous two inequalities to solve for IGZI yields equation
(30) and equation (31).

1.25V

(30) |G2l SW = 3.43
0.3V
(31) IG2IZW=L55
Combining the two inequalities and using IGZI = |- RI l/R9 | ,

(32) 1.553 |G2| = l- R11/R9 | $3.43

'44

Where R9 is chosen to have the standard input resistance of 10 KO"
equation (32) yields,

(33) 15.5KQS l-Rlll $34.3KS2

Choosing R1 1 = 33 K5) allows the digital board to use much of its
voltage range thus lessening round off error (see Section 1.2-2). IG2|

can be calculated from the resistor values as,

33 K52
(34-) |G2| = l- R11/R9 l = 10 K9 = 3.3 (10.4 dB)

 

The above equation, equation (28) and equation (29) combine to reveal
that ILPmI will exist in the range as calculated in equation (35) and

equation (36).

(35) ILPmI s )02) . 0.364V= 1.20v
(36) ILPml 2 I02) * 0.192V=0.64V

(Notice that this is within the log amp's operating range 0.3 V s ILPmI

s 1.25 V.)

The final design for the first stage is shown in Figure 25. It
utilizes the second op amp of the dual op amp that was used in the
design of the first stage (OP227). The component values of Figure 25
are listed in Table 6. A typical output from this second stage of

45

 

R10

 

 

 

R11

 

 

+5V

 

 

 

Figure 25. The Second Stage

Table 6. Second Stage Components

 

Resistor

R9
R10
R1 1

 

Kaine

10 K!)
7.5 K52
33 KS}

 

 

 

 

46

amplification is similar to that shown in Figure 14--where the output
voltage level is within the SCF system's acceptable range.

Section 2.3-3
Level Shift

In the last section it was shown that the SCF system's output
signal was limited to the magnitude of 1.25 V--thus limiting the SCF
system output signal to a 2.5 V voltage swing. Yet, between the analog
board and the digital board tlnere is an A/ D converter that will convert
signals that exist within the range from 0 V and 2.5 V (the current
signal varies between 11.25 V). A level shift is then added to the
design and is the topic of this section.

A level shift filtering scheme is shown in Figure 26. Here,
equation (37) is the result of applying Kirchoff‘s Voltage Law to an
ideal op amp circuit [20], [21].

Similarly, equation (38) results from an ideal op amp's inverting input
current being 0 A.

Using equation (37) to solve for I,

47

 

R16

 

 

 

 

 

 

 

 

 

 

Figure 26. Voltage Shifting Amp

V -V
Sin REP
(39) 1"“ R15

Inserting this equation into equation (38) and solving for V30ut’

Vain ' VREF
(40) V30“ = VREF - (R16 "‘ —_]Rl_5—_-)

R16
= VREF "' 'R'15'(VREF'V31n)

R18 R18
=VREF (1 +R15)'V3ln (R15)

So, if VREF is a positive DC voltage and R15=R16,

48

(41) V30ut = (2 I VREF) “Vain

Figure 26' illustrates the level shifting concept and is based on

the results of equation (41). The top portion of this figure represents
the level shift's input signal Nam), while the bottom portion shows a

possible output signal (Vsout). (Note that as VREF increases, the output
signal can be shifted so as to have all voltages be positive throughout
its entire voltage swing.)

The actual level shift amplifier design is shown in Figure 27.

Here, VREF is accessed from the center point of a potentiometer (R13)

whose voltage exists within the range of its end points (0V to 2.5V).

. \ /_\V“““/.,.
v v

 

 

2"‘V V

 

 

(for Vm > 0 V)

 

 

 

Figure 26'. Level Shift Results

49

 

R16

 

 

R15

 

 

 

 

+2.5V

R13

 

 

 

 

Figure 27. The Level Shift

Table 7. Level Shift Components

 

Resistor Value
R13 5 K52 pot.
R15 10 KS)

 

 

L R16 10 K9

 

50

The resistor is to be adjusted to a theoretical voltage of 1.25V (see
Appendix C - Trimming). All resistor values are shown in Table 7,
where R15=Rl6. Several signals from this level shift amplifier's
output are detailed in Section 2.4-3.

Section 2.4
Design Results

This section contains the heart and breatln monitor's analog
board design. First, Section 2.4-1 includes various schematics from
previous sections into a schematic that encompasses the entire analog
board's design. The monitor's power requirements and the power
design are then revealed in Section 2.4-2. The typical heart and
breath signals found at the analog system output are illustrated in
Section 2.4-3. (Trimming information for the analog board's hardware
is found in Appendix C.)

Section 2.4-1
The Analog Board

Various analog components have been detailed in the previous
sections and are consolidated in the overall analog design of Figure 28.
The detailed design schematics appear in Figure 29 through Figure
37. These figures make reference to various resistor values (Rx),
capacitor values (Cx) and components (Ux) which are listed in Table 8.

Table 9 and Table 10, respectively.

51

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Figure 29. First Part
R2

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Figure 30. First Stage

53

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 31.

Log Amp

 

54

 

 

 

 

 

 

 

 

 

 

 

Figure 32. Rivet Circuit

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R10

 

R11

 

+5V

 

 

 

Figure 33. Second Stage

 

 

56

 

 

 

 

 

 

FILTER our 3 0 LE“;
8
ILTER IN ,_
LKC} CIK 9
fcmR 3:6 VADJ _,
7
Clock A

 

 

 

 

 

 

 

Figures 34. Lowpass SCF

57

 

 

 

 

 

 

 

 

 

 

 

mom 890905 .mm 9:58
>m+ >m-
Bo Bo
ammo
m R -2 T; T: _m
+0> +<> ozo< AS -<> w
hm. a: .330 .: [Ail
mdnm OH mugs—O
B hm v30 I)
«mm m:
2
. em .2 2
am \ \ 202
IE. .3: .5 . a.
S
cum m 438:8 m
45.22 emu
mém m
. m em 8
Ba
_ 0 3
.3 >7: mm
Sm 2m

 

 

 

 

 

58

 

R16

 

 

R15

 

 

 

 

 

 

 

 

Figure 36. Level Shift

59

 

 

 

  

 

IFC
5V
3 (X U8
_E_
02410:
4
RN 0V

 

 

 

 

Digital Input
0

 

 

Sample
1 3
Rx"Ix-‘2).

20
1 1

 

 

 

 

U15

 

 

 

 

Figure 37 . Digital Preparation

 

60

Table 8. Analog Board Resistors

 

 

R13 = 5K pot.
R14 = 50 K pOt.

R i r = V 9 Dee in the eiregit,
R1 = 10 K input to inverting input on lst stage
R2 = 500 K forward loop in 1st stage (Gl=R2/R1)
R3 = 50 K pot. offset adjustment at 1st stage
R4 = 190 stabilizes non-inverting input at lst stage
R6 = 1 K pot. adjusts offset of log amp
R7 = 1M holds amp input at virtual ground
R8 = 1M specified by rivet's design
R9 = 10 K at inverting input at 2nd stage
R10 = 7.5 K stabilizes non-inverting input
R11 = 33 K forward loop in 2nd stage (02=R11/R9)

offset adjustment for level shift
ofi'set adjustment for lowpass SCF

R15 = 10 K input to inverting input on level shift
R16 = 10 K forward 100p in level shift (G=R16/R15)
Rl7-R22.5 = 10 K for highpass configuration, Gain=l

R23 = 8 K for chip select

R24 = 10 K pot.
R25 = 240

adjustment on regulator to produce +8.0V
allows current flow across Vout - ADJ

 

 

61

Table 9. Analog Board Capacitors

 

Canadictulalue W

C1 = 4.7 (IF "' reduces dc bias at front end

C3, C4 = 0.1 uF minimizes dc drift at lst stage
C5 = 0.1 ILF specified by rivet's design

C6, C7 = 0.1 uF minimizes dc drift at rivet

C8, C9 = 0.1 ILF minimizes dc drift at lowpass SCF

C10. C12 = 0.1 uF minimizes dc drift at log amp
C11, C13 = 15 ILF “ polarizes dc voltage at log amp

C14 = 0.1 uF , specified in rivet's design

C18, C19 = 0.1 uF minimizes dc drift at highpass SCF
C20 = 1000 pF for chip select

C21, C22 = 0.1 uF minimizes dc drift at sample-hold
C23 = 1000 pF sample-hold

C24 = 1 uF adjustment for piezo

C25. C26 =10 ILF " as specified for voltage converter
C27, C31,

C32 = 33 uF " polarizes dc voltage at power sources
C28’C309

C33-C36 = 0.1 uF minimizes dc drift at power sources

* tanly'tic capacitors

 

 

 

62

Table 10. Component Devices and Voltage Requirements

 

 

26213;

Ul- Low noise op amp,OP227
U2- Rivet op amp, LF356

U3- Bipolar log amp, 0E12910
U4- Lowpass SCF, MF6CN-100
U5- Highpass SCF, MFIOCN
U6- Sample and hold, LF398N
U7- Chip select, SN74122N
U8- Signal adjust, 74L8624

U9- DC/DC converter, ESIZTOS
U10- Voltage converter, Si7661cj
U l l - Voltage regulator,

LM317T

Ul2- Voltage regulator, AD580

U13- Microwave transceiver, MA86502

U 14- Power Source
U 1 5- Piezo
Digital Board

W
0 V, i5 V

0 V, :12 V

0 V, :12 V

0 V, 15 V, +2.5 V
0V, iSV

CV, :15 V

+5 V

0 V, +5 V

+9-18 V

0 V, +12 V

0 V, +12 V

0V, +8.0V

0 V, +8.0 V

+5 V
0 V, +2.5 V, +5 V

 

 

63

 

BREATH
(connects AB 8: C
at pin 2 and pin 3)

A

 

 

 

HEART
(connects A.B & C
at pin 1 and pin 2)

 

 

 

 

 

Figure 38. External Switch

The diagrams for three (3) poles to an external double throw
switch (see Figure 38) are individually shown in Figure 28. The two
possible switch positions are determined by the operator of the
monitor and result in the monitor's display representing either a heart
rate or a respiratory rate. The monitor functions so as to determine a
heart rate when the switch position creates a short circuit across pins
1 and 2. Short circuits are simultaneously created across 1A and 2A,
1B and 2B, and 1C and 2C; thus, connecting the rivet circuit into the
log amp's feedback loop, allowing both the lowpass and highpass
filtering of the signal and connecting a 0 V signal to a digital board
input.

Having registered the 0 V signal at the digital board, the
algorithm goes into the "heart processing mode" and implements the

64

following: the TI‘L clocks are adjusted to the frequencies required in
heart signal processing, the signal is sampled at the rate programmed
for collecting heart data, and the subject's heart rate is calculated from
the sampled data using the current heart rate algoritlnm.

The monitor functions to determine a respiratory rate when the
switch position creates a short circuit across pins 2 and 3. Short
circuits are simultaneously created across 2A and 3A, 2B and 3B, and
2C and 3C; thus, disconnecting the rivet circuit from the log amp's
feedback loop, bypassing the highpass filter and allowing only lowpass
filtering of the signal and connecting a +2.5 V DC signal to a digital
board input.

Having registered the +2.5V signal at the digital board, the
algorithm goes into the "breath processing mode" and implements the
following: the TI‘L clocks are adjusted to the frequencies required in
breath signal processing, the signal is sampled at the rate
programmed for collecting breath data, and the subject's heart rate is
calculated from the sampled data using the current breath rate
algorithm.

A schematic for A/ D conversion and the audible indication of the
monitor's analog output signal is contained in Figure 37. When the
digital board is ready to accept another data sample, it sends a signal
to the chip select pin at a monostable vibrator (SN74122 - Texas
Instruments). 'Ihis chip select (at U7) then triggers a sample-and-
hold device (LF398 - National Senniconductor) to sample its incoming
analog signal and hold its value (for a time dependent on C23), while
the A/D performs its sampling. A speaker (piezo-U15) then uses the

65

analog signal (from U8) to convert a DC voltage into an audible sound
convenient to the operator.

Finally, the interface between the analog board and digital board
is provided through a ribbon cable whose pin connections are shown

in Figure 39. (These connections are from the perspective of the

analog board.)

 

Heart/ Breath Sample

 

Voltage Trigger
S l (1 (pin 1)
51:35: I N/C Clock B
_ l - , .l-L (Highpass)
2 4 6 8 10
1 3 5 7 9 (Lowpass)

 

 

 

1)—

l l l _l'l_
6 L—-> Clock A

Figure 39. Ribbon Cable Interface

 

 

 

Section 2.4-2
The Power System

The monitor's power system design was developed while the
power requirements for the monitor's various devices grew and
changed. The final result is that it supports all monitor components
which require the following voltages: 0 V, +2.5 V, :5 V, +8.0 V and
:12 V (see Table 10). (Note, that the log amp can theoretically
operate with supply voltages in the range of 15 V to 3:15 V. However,
when the voltage source of :l:5 V was tested, the device did not

66

perform adequately. The voltage chosen (i12 V) was readily available
from the power supply as it was designed, and was also acceptable for
proper log amp operation.)

The digital board draws most of the current in the monitor.
Although its current drain is expected to drop with additional use of
CMOS devices [9], the digital board currently drains a maximum of 1.0
A at 5 V. The transceiver is the second largest user of power supply
current (requiring a maximum of 200 mA). The exclusive use of CMOS
technology in the remaining analog board design results in a minimal
drain on the power supply current (< 100 mA for all other analog
board components and the components in the power system itself).

The power design is shown in Figure 40, Figure 41, Figure 42
and Figure 43. These figures will reference various resistor values
(Rx), capacitor values (Cx) and components (Ux) which are listed in
Table 8, Table 9 and Table 10, respectively.

Central to the power system is the DC/ DC converter shown in
Figure 40: this supplies the monitor with :15 V, +12 V and ground
(0V) from a source supply DC voltage between 9 V and 18 V. The
converter is capable of delivering 15 Watts of power, and typically
supplies 1 .5 Amps of current. A relatively compact rechargeable
battery is used as the portable voltage source for this converter.

The remaining required voltages are supplied through another
voltage converter and several voltage regulators. The voltage converter
of Figure 41 accepts a positive DC voltage (+12V) and inverts it to
provide the corresponding negative voltage (of -12 V). Figure 42
shows a voltage regulator which uses a potentiometer adjustment to

provide the +8.0 V required at the monitor's transceiver. (See

67

 

 

 

 

 

 

+12V ‘
rm“
. o .
'U
> +5V
00
’1‘
j G)
E-vm 0ND
U9
-5V .

 

 

 

 

 

 

 

Figure 40. DC/DC Converter (0V,:5V,+12V)

Appendix C-Trimming). The voltage regulator scheme of Figure 43
produces +2.5 V from the mean of its two DC voltage inputs (0V and
5V).

This power design has produced all of the voltages required of
the monitor's various components (see Table 10), while also supplying

enough current to the monitor [22].

68

 

 

C25

 

 

+12V
8
+V -12V
2 +0 v 5 >
:1:— mo \l-x C26
- -C GND
4 3

 

 

 

 

Figure 41. Voltage Converter (-12V)

 

+12V

 

 

 

3 En

 

Vout .

 

 

R25

\L+

 

 

 

 

Figure 42. Voltage Regulator (+8.0V)

 

 

69

 

 

 

 

 

 

 

 

 

 

O
+5V 1
E)-
+2.5V
2
U12 OUT '
E- A
C30

3

Figure 43. Voltage Regulator (+2.5V)

Section 2.4-3
Analog Output Signals

A circuit board had been designed to contain the the analog
board and the power supply components of the monitor. [A housing
for the entire monitor (transceiver, analog board, digital board, L.E.D.s
and switches) was then fabricated using an aluminum box (3"x9"x5").
The flat patch antenna was epoxied to the bottomside of the box and
surrounded with a microwave absorbent foam so as to minimize the
monitor movement on the subject's chest and the effect of movement
in the subject's immediate area. Also, a shell program was burned
into the digital board's EPROM to test whetlner the external switch
would properly signal the digital board to alter its 'ITL clock

frequencies] The monitor was then placed in the center of several

70

subjects' chests, while a PC controlled sampling device collected data
from the analog board. This section will show the plots of some of the
typical heart and breath data that was collected.

The heart type signals represented here, have been sampled at
64 Hz (see Appendix D for a discussion of the constraints on sampling
frequency), and have the mean extracted from the data. The signals
have also all been filtered by the switched capacitor filters with the
cutoffs set at 5 Hz (lnighpass) and 20 Hz (lowpass). [This filtering
scheme was suggested by those who processed the digital heart signal
as the heart signal has an impulsive nature. Tlnus, the fundamental
frequency can be filtered off (along with noise due to breathing) and
the heart rate can still be determined from the harmonics in the
signal's spectrum.)

Data was simultaneously collected at the output to the first stage
(V but) and the analog board's output (V 30,“), while a pulser (a crude
mechanical model replicating a heart's impulsive movements, set to
move at 80-85 Hz) was placed in front of the monitor's microwave
antenna. As these signals represent the input and the output of the
analog board, a comparison of the signals can reveal the effect of the
analog board on an impulsive (heartlike) signal.

The resulting data plots are shown in Figure 44 and Figure 45.
These plots are in many ways very similar: both appear impulsive and
the frequency of the pulses are alike (there are 46 points of data
between the first two impulses of each plot). However, the minor
oscillations at the input (less than 20% of the magnitude of the input
pulse) become a substantial part of the output signal at the output

71

 

 

 

 

 

 

 

 

 

 

 

I
WWI- WW4) [WWW [MM
'5 ‘5‘
3
g .
8
E, -15-
H
5.
.5
ti
-35 - u . r
o 100 200
Sample Number (@ 64 Hz)

 

 

 

Figure 44. Pulser: V1,mt (Output of the First Stage)

72

 

200-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 -
3
.2 J"
2
3 ° -
3
§ ~100 '1
:
-200 -
-300
0

I ' l
100 200

Sample Number (@ 64 Hz)

 

V Figure 45. Pulser: V30,“ (Output of the Analog Board)

 

73

(where the oscillations have a magnitude that is roughly 70% of the
magnitude of the output pulse).

The next two figures show plots of an actual heart signal at the
analog board's output (Figure 46) and the absolute value of that signal
with the mean subtracted from each data point (Figure 47). These two
signal plots show heart signals occurring at a frequency rate of 1.576
H2. [’lhere are 203 sample points, or (+ 64 samples per second =)
3.172 seconds of data for 5 heart beat cycles. With 5 heart beat cycles
for 3.172 seconds, the heart rate is 1.576 cycles per second (Hz).]
And, although this rate can be seen, it is not always revealed in the
processing of the data--especially when the heart rate is lower than
the subject's respiratory rate. The heart signal is therefore
bandpassed at 5-20 Hz, where the fundamental frequency is obvious in
the power spectrum of its absolute value. [See Figure 48 and Figure 49
for a comparison of the power spectra (using 256 points, no zeros, 1
segment and a rectangular window) of the original signal and its
absolute value, respectively. Notice that Figure 48 has its first major
peak at point 20, which corresponds to 4.75 Hz. Figure 49, however,
has its first power concentration at point 7, which corresponds to 1.5
Hz. (For each of the past two figures, the power spectra has a
frequency resolution of 0.25 Hz, and the first point represents point
zero. See Section 3.3 for more information about power spectrum

analysis, as it relates to breath signals.)]

74

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100- h
A l ‘
8 ~ I
:3 o- I
o I
5 I
8
9‘- .
E
'5' -100-
"I
III

I
-200 I . u - u . fl
0 100 200 300

Sample Number (@ 64 Hz)

 

 

 

Figure 46. Heart Signal: V3,,ut (Output of the Analog Board)

75

 

 

 

 

 

 

 

 

 

 

 

 

 

150 -
33
i
a
'5'.
E.
3
3 50 -
'3
i
a
-50

 

 

I ' I
100 200

Sample Number (@ 64 Hz)

300

 

Figure 47. Absolute Value of the Heart Signal

 

76

 

 

 

 

 

 

 

 

 

1500 1
III
E I
I:
'5 1000 -
I I I
6' 500 -
8 ' L

0 1 ' I
0 4
hequency (Hz)

 

 

 

Figure 48. Power Spectrum of the Heart Signal

 

400 -

 

 

 

 

 

 

 

 

I:
a I
2
o
g 200-
g
m
In
3
8
0T 4'

 

Fn'equency (Hz)

 

 

 

Figure 49. Power Spectrum of I Heart I

77

The remainder of this section will show plots of breath data that
had been collected at the analog board's output (Vaout) for various
subjects, sampled at 32 Hz (see Appendix D for a discussion of the
constraints on sampling frequency), and had the mean extracted from
the signal. The data collection occurred while the monitor's external
switch was in the breathing position and the lowpass switched
capacitor filter was configured for a cutoff frequency of 3 Hz. The
breath plots appear in Figure 50, Figure 51 and Figure 52, and will be
described in more detail and then processed by various algorithms, in
Chapter Three.

78

 

300-

100'"I

~100‘

Analog Output (Relative Volts)
O

-200-

. M IW

r #1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-300

 

' fi 1

i ' I
200 400 600

Sample Number (@ 32 Hz)

 

Figure 50. Breath Signal #1

 

79

 

200q

100-

 

Analog Output (Relative Volts)
O

-100' I

Iwaw II

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-200 v r ' l l
0 200 400 600

Sample Number (@ 32 Hz)

 

 

 

Figure 51. Breath Signal #2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IuIIhIIIIuI-in
W II
U
# n
NV
r1“
M.
kn)
Fl
I“
U.
IhI
M
IMI
IJIv
LII
IIUW
M .
Mil
h
....... “Ilia
m m
.3 ob 533—5 253

 

 

200 400
Sample Number (@ 32 Hz)

 

Chapter 3
Processing the Breath Signal

Past monitor designs have only been concerned with the
filtering, processing and rate calculation of a heart signal. The breath
signal was not filtered, nor was the signal processed by algorithms
which would determine the respiratory rate of the subject. The filter
design, however, has become flexible enough to filter eitlner a subject's
heart or respiratory signal. The current monitor thus requires an
algorithm for determining respiratory rates from a breath signal.

Four different schemes for determining the breath rate from the
filtered and digitized breath signal will be discussed in Chapter Three.
The four algoritlnms methods include: integration, auto-correlation,
power spectrum analysis and recursive maximum likelihood (RML)
estimation. Each algorithm will be summarized and used to calculate
the respiratory rate of five different signals, including: three actual
breath signals which were collected at the analog board's output, a
non-filtered breath signal from the analog board's input (Vlout) and a
signal which is the sum of a cosine and noise.

The three breath signals have been plotted in Figure 50, Figure
5 1 and Figure 52: the analog's input signal (the non-filtered breath
signal referred to earlier) is plotted in Figure 53; and, the sum of a
cosine (of magnitude=1 and frequency = 1 Hz) and Gaussian Noise

(mean = 0 and variance = 4) is shown in Figure 54. (See Section 4.2

81

82

 

 

1001 h

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I

i

13)

E.

‘2'.“

.5

i

400 ' I ' l ' l
0 200 400 600

Sample Number (@ 32 Hz)

 

Figure 53. Analog Input (#4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cosme + Gausian Noise (Relative Volts)
O

 

 

’8 V i r I v 1 u
0 50 100 150 200

 

Sample Number (@ 32 Hz)

 

 

Figure 54. Cosine + Noise (#5)

84

for a comparative analysis of the algorithms.)

Each of the last five signals visibly reveal some form of high
frequency components which are not a direct result of breathing or its
simulation (as in signal #5). (The components are seen throughout the
plots of signals #4 and #5, and near sample numbers 300, 400 and
500 in signals #1, #2 and #3, respectively). These high frequency
components represent the portion of the signal due to the heart and
backgound movement existing near the subject.

These non-breath components can be visually removed from the
signals-~thus allowing a human to visualize the portion of the signals
which are due to the breathing. This visualizing has resulted in Table
1 1, which is labeled "ideal signal characteristics." This table holds the
optimum values for both frequency and breaths per nninute for each of
the signals. Thus, algorithmic calculations are to be compared to the
values found in Table l 1.

EXAMPLE CALCULATIONS FOR TABLE I 1 (using the data of Figure
50):

 

 

(42) mud—S _ #samples , M , 2--half cycles
. Cycle " # half cycles 32 samples cycle

(615 ... 7) t (1 + 32) "' (2) = 5.49107 S_____ecc;tncrln;is

cles Seconds 1
(43) Frequency (or 89%;? or Hz) = 1 + W = 5719 Hz

= 0.1821 Hz

85

Table l 1. Ideal Signal Characteristics

 

t

 

 

 

 

 

 

 

 

 

 

 

 

Total # of # of
# of full samples/ seconds Frequency
Figure # 1/2 cycles 1 /2 cycles per cycle (Hz) B.P.M
50 7 615 5.49 0.18 10.8
51 14 610 2.72 0.37 22.2
52 19 597 1.96 0.51 30.6
53 l 1 581 3.30 0.30 18.0
54 12 192 1.00 1.00 60.0
" All signals were sampled at 32 Hz.
Table 12. Actual Signal Characteristics
# of Samples # Of it
Zero Crossings between seconds Frequency
Figure # '1 crossings per cycle (Hz) B.P.M
50 9 615 4.27 0.23 13.8
51 16 610 2.38 0.42 25.2
52 21 597 1.78 0.56 33.6
53 13 I 581 2.79 0.38 21.8
54 85 198 0.15 6.67 400

 

 

 

 

 

 

" All signals were sampled at 32 Hz,
and 2 crossings per breath cycle are assumed.

 

 

 

86

# of Cycles or Breaths
(44) B.P.M. (or Minute )

_ # of Cycles ‘ 60 seconds

Second minute

 

= [(0.18) r 60 = 10.8] B.P.M.

Table 12 reveals the actual frequencies and breatlns per minute
that might have resulted for the signals if zero crossing detection were
implemented without visually removing the high frequency
components. [Equations (42)-(44) also apply here.]

Section 3.1

Integration

This section will look at the effect that integration has on
suppressing the unwanted higher frequency components [23] found in
the five signals of Figures 50-54. The integation of a digitized signal
over a particular time period M) is determined by calculations
similar to equation (45) [24].

k'i‘
(45) iju) = 'r *1 x(l) + 'r * x(2) + + 'r * x(k)

k
= T " 2 x(n)
n=1

87

[Specifically for the breath signals: k is the number of samples (640),
T is amount of time per sample (1/32 seconds for the five breath
signals) and x(n) is the magnitude of the nth sample of data.)

The value of T is a constant, positive scalar, and can not affect
the sign of this integration summation. 'Iherefore, since this exercise
is meant to determine sign changes of the integrated signal (a zero
crossing), T will be normalized to l and the integation of the breath
signals will be approximated by their proportional running sums.

The next five figures (Figure 55, Figure 56, Figure 57, Figure 58
and Figure 59) are the result of computing the running sum and tlnen
subtracting the mean of the running sum from the data plotted in
Figure 50, Figure 51, Figure 52, Figure 53 and Figure 54, respectively.
(As the signals do not occur as positive and negative magnitudes for
equal time periods, the mean has been subtracted from the running
sums. Also, a commercial software package [25] has been used in

performing the calculations needed for plotting the data.)

88

 

 

 

 

I
r #1
15000 -
2’
o
>
i
5000 -
i!
E.
S
8
E -5000 -
H
.5
-15000 . . . . . ,
j 0 200 400 600
“ Sample Number (0 32 Hz)

 

 

Figure 55. Integated Breath Signal #1

89

 

4000 -
h r #2

..... I I I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Integration - Mean (Relative Volts)

 

 

 

 

 

 

 

 

 

 

I ) ) ) )

 

 

 

 

 

“4000 1 ' 1 r I ' l
0 200- 400 600
Sample Number (@ 32 Hz)

 

 

 

Figire 56. Integated Breath Signal #2

9O

 

 

 

 

 

 

 

 

 

6000 -
Breath #3
4000 q
2%
>
o
.5 2000 -
%
E.
E?
E o 4
8
E
o
H - ..
5 2000
-4000 T I ' I ' f
0 200 400 600
Sample Number (@ 32 Hz)

 

 

 

Figure 57. Integrated Breath Signal #3

91

 

 

 

 

 

 

 

 

 

 

 

 

2000 -
An In 11

1500 -
3 1000-J
o
> n
o
> I
I! 500
'5 T
E.
i o-
S
8
E -m-
H
a -1000-

-1500 v 1 ' l ‘ I

0 200 400 600
Sample Number (@ 32 Hz)

 

 

 

Figure 58. Integrated Analog Input (#4)

92

 

 

 

 

 

 

20 "'
E
'3 10 . Qg§ln§ + NQ1§§
>
3 w
3
S
0 O "'
E.
S
I '10 "'
a
a q
3 -20 "‘
.5
-30 u
'40 ' l - l
O 100 200

 

Sample Number (@ 32 Hz)

 

 

Figure 59. Integrated Cosine + Noise (#5)

93

The rate of the previous integrated signals can be determined in

an on-line program, through the use of zero-crossing detection of the

signal. The integrated signals' characteristics are summarized in

Table 13, wherein the number of breaths (or cycles) per minute were

calculated as in equations (42)-(44).

Table 13. Integrated Signal Characteristics

 

 

 

 

 

 

 

 

 

and 2 crossings per breath cycle are assumed.

# of I Samples # Of 1.
Zero Crossings between seconds Frequency
Figure # '1 crossings per cycle (Hz) B.P.M
55 6 494 5.15 0.19 11.4
56 13 567 2.73 0.37 22.2
57 16 485 1.89 0.53 31.8
58 12 612 3.19 0.31 18.6
59 l l 134 0.76 1.32 79.2
"‘ All signals were sampled at 32 Hz,

 

(The results of the method of integration on the five signals have been

shown in this section. However, Section 4.2 will provide further

discussion and comparisons related to this and the other three

processing methods.)

 

Section 3.2

Auto2correlation

The auto-correlation, Rxx (B), of a function x(t), is the expected
value of the product of x(t) and x(t+fi)--where ,8 is a lag in time [26].
Below, equation (46) shows the autocorrelation function for a sampled
signal, x(n) [27].

N-l
(46) Rxx (.8) = 2 x(n)x(n-15)

n=0

[Where, N is the number of samples in a record, n is the nth sample of
the record and 13 is the autocorrelation time lag (,6 is assumed to be a

multiple of the sampling time (T). or 15 * T).]
The value of Rxx (B) is a measure of how much x(t) and x(t+15)

are similar to each other. It depends on the delay 15, and is always a
maximum for 15:0 [28]. This is because Rxx (0) is the expected‘value
0f x(n)‘x(n+0) = 2(n), which is positive for all n. Thus, while the
functions in Figure 60 and Figure 61 are all sinusoids sampled at 32
Hz, the two functions in Figure 60 represent sinusoids that are in-
phase with each other, and the two functions in Figure 61 represent
sinusoids that are out-of-phase with each other. Therefore, if equation

(46) were applied to the signals shown , then the largest possible
value for Rxx (B) would result for the signals of Figure 60, and the

most negative value for Rxx (15) would result for the signals of Figure

61.

94

95

 

Sine(x1c/32)

 

 

 

Sine(x1c/32)

 

 

 

 

Sample Number (@ 32 Hz)

 

 

 

Figure 60. Sinusoids: In Phase (6:0)

96

 

Sine(x1I/32)

 

 

 

 

 

Sine(1tx/ 32 + 1:)
O
O

.<'>
01
1

 

 

 

 

-1.0 1 ' I I I
0 10 20 30

Sample Number (@ 32 Hz)

 

 

 

 

Figure 61. Sinusoids: Out of Phase (15:16)

97

Auto-correlation has been performed on the data signals of
Figures 50-54, using a commercial software package [25]. The
software package calculated a normalized auto-correlation function (so
that Rxx (0)=1) for all five data signals, using the following: 640 sample
points. a maximum lag of 320 sample points and 0 offset points. The
resulting auto-correlations for the data of Figure 50, Figure 51, Figure
52, Figure 53 and Figure 54 are plotted in Figure 62, Figure 63, Figure
64, Figure 65 and Figure 66, respectively.

98

 

 

 

 

1.0 -
sample number = 186

0.5 -
8 0.0 -
3 4
-0.5 -

-l.0 u ' I f

0 100 200 300

LAG-Sample Number (@ 32 Hz)

 

Figure 62. Auto-correlation of Breath #1

 

99

 

sample number = 88

0d

Rn(LAG)

 

 

f r W I I r

I
0 100 200 300

LAG-Sample Number (@ 32 Hz)

 

 

 

Figure 63. Auto-correlation of Breath #2

100

 

1 0
1‘ sample number = 62

A A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A
g 0.0 .
E
-O.5 .
-l.0 ' I I I f I fl
0 100 200 300

LAG-Sample Number (0 32 Hz)

 

 

Figure 64. Auto-correlation of Breath #3

101

 

 

 

sample number = 105
1.00
0.50 -
8
3 0.00 .
-o.5oJ
'1-00 ' I ' I I I
0 100 200 300
LAG-Sample Number (@ 32 Hz)

 

 

 

Figure 65. Auto-correlation of Analog Input (#4)

102

 

 

 

 

1.00 -
0.75 1
0'50 - sample number = 32
E?
E 0.25 -
. I
0.00 - I. ‘ 1 i
1
-o.25 - . . . . .
0 100 200 300
LAG-Sample Number (@ 32 Hz)

 

 

 

Figure 66. Auto-correlation of Cosine + Noise (#5)

103

Table 14. Auto-correlation Characteristics

 

 

 

 

 

 

 

 

 

# of "
RXX(LAG) LAG. or
seconds
at lst peak, Sample 1 Frequency
e
Figure # for LAG > 0 Number per cyc (HZ) B.P.M
62 0.78 186 5.81 0.17 10.2
63 0.85 88 2.75 0.36 21.6
64 0.79 62 1.94 0.52 31.2
65 0.90 105 3.28 0.30 18.0
66 0.20 32 1.00 1.00 60.0
* All signals were sampled at 32 Hz.

 

 

 

The rate of the original signals can now be determined from
their auto-correlation functions. using equations (43)-(44) and
calculating the number of seconds per cycle using equation (47). And.

the results of the auto-correlation are shown in Table 14.

Seconds _ #samples or LAG . 1 second

Cycle " lst peak in RX): (15) 32 samples

 

(47)

 

(= 186 + 32 = 5.8125, for Figure 62)

[This equation is based on the the signals, x(n) and x(n+fi), being most
similar (Rxx (,6) is largest) after they have been shifted for as many

samples as make up a cycle for x(n). Also, the results of applying the

auto-correlation method to the five signals have been shown in this

l 0 4
section. However. Section 4.2 will provide further discussion and
comparisons related to this and the other three processing methods.)

Section 3.3
Power Spectrum Analysis

The power spectrum of a signal, x(n), is Su(m)--which is also
the Fourier transform of the signal's auto-correlation, Rum) [29].

Therefore, once the auto-correlation of a signal, x(n), has been
determined. its power spectrum can be calculated and the frequency
of primary power concentration in the signal can be determined.

One method of calculating a power spectrum is by a discrete
Fourier transform (DFT), which applies the relationships of equation
(48) and equation (49) to an auto-correlation funtion [30].

N-l

(48) Karla) = 20 x(nT) ill e'janT
n:

(49) = “13%?

(Where, N is the number of samples in the signal. sampled every T
seconds, (2 is the frequency resolution of the spectrum, n represents
the nth sample of a total number of N, and m is the mth discrete
spectral component [31].)

The power spectra of the five signals [in Figures 50-54) have been
determined using a commercial software package [25]. This package
calculated the power spectra using either a DFT or fast Fourier

105

transform (FFT), having the following variables: 512 points/segment,
0 offset points, 1 segment, 0 inserted zeros and a rectangular window.
(512 points is used as powers of two yield more efficient FFT
calculations [32].) Also, as all signals had been sampled at 32 Hz, then
T = 1/32 (and N = 512), so that Q = 32/512 =0.0625 Hz. The next
five figures (Figure 67, Figure 68, Figure 69, Figure 70 and Figure 71)
are the power spectra that resulted from the signals previously shown

in Figure 50, Figure 51, Figure 52, Figure 53 and Figure 54.

 

respectively.

The results of the spectral analyses are summarized in Table 15,
where the major spikes of power in each spectrum are interpreted as
occuring at the original signal's frequency. However, for further
discussion and comparisons related to spectral analysis and the other

three methods, see Section 4.2.

106

 

 

 

 

 

 

 

 

 

 

5e+5-
464-5" \ Om:
3e+54
a
E 2e+5-
m
le+5-
0e+0 T M” 7 2“'I-'—-n
0 2 4 6 8 10 12 14 16 18 20
m (frequency resolution. (2 = 0.0625 Hz)
Figure 67. Power Spectrum of Breath Signal #1
264-6" \
m:
E
E le+6-
(I)
0e+0 :4. .-;:;<;:;:?*‘:.
0 2 4 6 8 10 12 14 16 18 20
m (frequency resolution, 9 = 0.0625 Hz)

 

 

 

Figure 68. Power Spectrum of Breath Signal #2

 

 

107

 

2&k+5-

1xk+5-

Sxx(m)

 

 

 

oxk+oqp—q¢=;=q-§===::F=J

0 2 4 6 8 . 10 12 14 16 18 20
m (frequency resolution, 52 = 0.0625 Hz)

 

 

 

 

Figure 69. Power Spectrum of Breath Signal #3

 

2&k+4'

]\

=5

 

 

 

 

 

 

H 0.0640 «4— “ A

O 4 8 12 16 2O 24 28 32

m (frequency resolution. 9 = 0.0625 Hz)

 

 

 

Figure 70. Power Spectrum of Analog Input (#4)

1'08

 

10‘

Sn(m)

 

O

 

4

 

 

 

.MM

 

8 12 16 20 24 28 32

m (frequency resolution, (2 = 0.0625 Hz)

 

Figure 71. Power Spectrum of Cosine + Noise (#5)

 

109

Table 15. Power Spectrum Characteristics

 

 

 

 

 

 

 

 

Frequency
ma
Fi # S (2 Hz H
gure xx(m) m ( ) ( z) B.P.M

67 4.6e+5 3 0.0625 0.1875 11.3
68 2.1645 6 0.0625 0.375 22.5
69 2.0e+5 8 0.0625 0.500 30.0
70 1.9e+4 5 0.0625 0.3125 18.8
7 1 12.9 1 6 0.0625 1.00 60.0
All original signals were sampled at 32 Hz,

and 512 points/segment, 0 offset, 1 segment, 0 inserted zeros
and a rectangular window were used in determining the spectra.

 

 

 

Section 3.4
Recursive Maximum Likelihood Estimation

Maximum likelihood estimation (RML) is used in situations
where the signal values (Y1, Y2, . .
sample are known, and have density functions [leb’fi 6)] dependent on

. , YN) resulting from a random

some unknown value of Q. A value for Q is estimated through the
maximization of the likelihood function, LM). which is also the joint
density function of the Yis [33], [34].

An RML algorithm has been developed which uses autoregressive
moving-average (ARMA) spectral estimation and is summarized

throughout equations (50)-(61) [35], [36].
A process, yt, can be descibed by the following ARMA model.

110

NA NC
(50) Yt= ' 2 ai.yt-i"' Z Ci‘ut-HUt
i=1 i=1

[Where, Yt is the process to be modeled (the analog board's output
signal in this application), “t is a zero mean uncorrelated random

sequence with variance, var(u), a1 and c1 are the model's coefficient

parameters, and NA and NC represent the number of respective poles
and zeros that are required to accurately represent the order of the

process.)
If 2'1 represents a unit delay (Yt- 1 = Yt "‘ z’l), then

 

(51) Yt=:((::1; " t

Where,

(52) A(Z'1)= l+a1 "'z'1-I-...+aNA"‘z'NA
(53) C(Z'1)= 1+c1 “'z'1+...+cNC"'z'NC

The model's vector of filter coefficients is denoted as in equation

(54).

(54) g = [ a1. a2, 0 . .. aNA, C1, C2, . o ., CNC 1T

 

111

The model's filter coefficients are updated at each data sample,
based upon the actual data and the filtered data [see equation (56) and

equation (57), respectively], and are notated as in equation (55).

(55) ¢t = [81, 82, . . ., aNA, c1, c2, . . ., °Nc ]T

The data vector,
(55) Yt =I'Yt-12 - - .. 'yt-NA' fit-12 - - 22 et-NA1T

and the filtered data vector,
(57) Yt =l'yt-12 - - ~° 'Yt-NA2 °t-1° - - .. et-NA 1T

(Here, Ct and et represent the actual and filtered (predicted) error.)

The values °t and 7t are calculated using equation (58) and

equation (59).
(58) yt=(1/Ct(k2'1))*yt
(59) et=(1/Ct(kz'l))‘et

Where the filter Ct (kz’l) uses the current coefficients of ¢t and is as

in equation (60).

(60) Ct (kz'l) = 1 +.k"‘ c1(t) z'1 + . . . + kNC“ cNC(t) z'NC

l 12
At any given sample, a spectral estimate for the breath signal, yt,

can then be determined from the estimated filter coefficients, as in
equation (61). Further analysis of the spectrum (as in Section 3.3)
reveals the signal's frequency, and thus the breathing rate.

C(z'l) “ C(z) |
A(z-1) '2 A(z) Z=6‘“’

(6 l) Sy(W) = var2(u) ‘
A program was written based on the previously described

algorithm, and can be found in Appendix E. (The initial conditions
that are used in the algorithm are that all values in the vectors a, Yt

and Yt are zero, NC=3, NA=3 and k=1.) The data of the five example

signals (plotted in Figure 50, Figure 51, Figure 52, Figure 53 and
Figure 54) have been processed by this program, with results as
summarized in Table 16 (for respective signals: #1, #2, #3, #4 and #5).

For further discussion and comparisons, see Section 4.2.

Table 16. RML Results

113

 

 

 

 

 

 

 

 

 

 

 

RML Breath Rate Estimate (B.P.M.)
Elapsed Signal Signal Signal Signal Signal
Time (sec) #1 #2 #3 #4 #5
1 384.9 353.2 332.6 1 12.1 409.4
2 385.3 380.7 255.2 1 13.9
3 383.9 396.5 206.9 128.7 1
4 4.1 402.4 182.7 1 14.6 Overflow
5 27.7 357.2 180.5 95.1
6 34.8 352.0 54.8 1 18.1
7 20.9 335.6 1 18.6 1 18.8
8 24.7 329.2 120.6 123.3
9 27.5 334.3 167.5 143.1
10 12.3 334. 1 178.2 144.9
1 1 8.6 325. 1 184.7 144.9
12 12.9 328.6 187.7 154.4
13 8.3 471. 1 198.8 163.9
14 3.3 61.8 199.0 158.5
15 7.8 39.0 182.5 152.8
16 10.7 49.0 183.8 148.6
17 7.8 111.4 171.7 145.7
18 13.3 1 10.6 163.9 141.8
19 11.2 131.9 166.3 144.7 L
20 12.0 145.7 182.3 145.2

 

 

Chapter Four

Conclusions

This last chapter provides conclusions on the analog board
design (Section 4.1) and the rate calculation of the respiratory signal
(section 4.2).

Section 4.1
Conclusions: Analog Design

The monitor's analog board filters the heart and breath signals,
80 that a digital board might further process and estimate a heart or
breath rate. The primary considerations in the design has been the
need to reduce the dynamic range (from the analog board's input to
the input of the digital board), and the special flexibility required in
filtering two different type of signals (heart and breath), occuring at
different magnitudes, and at different frequency ranges.

The design has allowed the analog board to be flexible in its
filtering, through the use of the lowpass and highpass switched
capacitor filters. These filters have algorithm controlled cutoff
frequencies, which are set through the programming of the digital
board. Previously. the cutoff frequencies have remained constant for
heart or breath rate processing. However, the flexibility of the
monitor could be increased through the use of more sophisticated

algorithms, with the ability to make changes in the digital board

114

115

generated clocks (perhaps, dependent on the outcome of the rate of
each processed signal). '

The monitor's dynamic range has been altered through the use
of a non-linear logarithmic device. This device has the effect of having
applied a variable amount of gain, depending on the magnitude of the
signal. The results of using the logarithmic amplifier in the analog
board design are demonstrated in Table 17. This table lists the
expected voltage ranges at different locations on the analog board (as
illustrated along with Figure 72).

As for possible changes that could be made to any future analog
board designs: more CMOS devices and a lower powered transceiver
should be incorporated into the design, the source of the oscillations
seen in the breath signal could be determined and reduced, and the
dynamic range at the anaolg board's input could be increased by
recalculation of the component values in the design of the hardware.
[It is suggested that 50 11V replace the 100 [IV minimum voltage level
for the lst stage's input (shown as "location A" of Table 17 and Figure
72).]

116

Table 17. Expected Input Ranges Throughout the Analog Board

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n\ D

I L08 AmH 2nd Stage

 

 

 

 

 

 

 

Analog Voltage Range (magnitude) => dB range Gain from
Location previous device
A 10011V - 20 mV 46.02 -
B 5 mV - 1 V 46.02 34.0 dB
C 192 mV - 364 mV 5.55 variable
D 634 mV - 1.20 V 5.55 10.4 dB
E 634 mV - 1.20 V 5.55 0 dB
F 1.89 V - 2.45 V 5.55 0 dB
1 Front End E/'{ Level Shift
A F
f \ Switched l
I Is t Stage Capacitor
7 Filters

 

Figure72. Locations in the Analog Board

 

 

Section 4.2
Conclusions: Respiratory Processing

Chapter Three investigated four different algorithmic methods
for processing respiratory signals: integration, auto-correlation, power
spectrum analysis and recursive maximum likelihood estimation. Each
of these algorithmic methods was appied to five individual sets of data
(plotted in Figures 50-54), and the resulting breathing rate was then
recorded in the methods' respective sections. Here, the rates that
resulted from each algorithm are summarized in Table 18 (in units of
B.P.M., or breaths per minute).

[From Chapter Three, the "ideal" rate of the signal is considered that
rate as determined by visually recognizing the frequency of the breath
signal's cycle. The "actual" rate of the signal is then considered the
rate calculated from the number of samples and the number of zero
crossings that occur over these samples. Overall, it is desirable for the
rate estimates to match those rates shown in the "ideal" column.

The application of the method of integration to these data
resulted in some improvement. These rates are quite close to the
ideal rates for all of the signals, except where the signal was a cosine +
noise (Figure 54). Overall, the integrated signals often wandered to
either the positive or negative, and the resulting plots don't show
integrated signals that could be relied upon enough to recommend
this method (without reservations).

The methods of auto-correlation and spectral analysis, resulted

in rates that are an improvement over those obtained from the actual

117

Table 18. Algorithm Breath Rate Summary

 

 

 

t Difi'erent Algorithms Breath Rate Estimate (B.P.M.)
a) (after approximately 20 seconds) _
"" Ze A t S tr RML
m Ideal Crossr0 s Integration! u 0 nl pec all

' (Actu Correlatio Analysis Estimation
50 10.8 13.8 11.4 10.2 11.3 12.0
51 22.2 25.2 22.2 21.6 22.5 145.7
52 30.6 33.6 31.8 31.2 30.0 182.3
53 18.0 21.6 18.0 18.0 18.8 145.2
54 60.0 400 60.0 60.0 60.0 -

 

 

 

 

 

 

 

 

 

signal. The rates are also quite close to the ideal rates. And, although
either of these methods could be recommended, the spectral analysis
is less desirable, as it must calculate a spectrum from an already
obtained auto-correlation function. Therefore, the auto-correlation
method is the processing method that is recommended for obtaining
breath rates for this heart and breath monitor.

As for the recursive maximum likelihood estimation, the results
were reasonably close to the ideal breath rate in only one of the five
cases. These results are not acceptable when compared to the other
three methods. This method is not currently being recommended.

However, RML estimation should not be abandoned as there are
several possibile explanations for the algorithm's inaccuracy: the
breath signal may require a model of greater order (currently, NA=3
and NC=3), the prefilter, C(z'l), may have become unstable (as it can
for the case where k=1) and the likelihood function may have detected

"false" maxima [35], [36]. Also, the data collection time period used

118

(20 seconds) may not give the algorithm as much time as it requires to
calculate breath rates (yet, there is no indication that extending the

processing time past 20 seconds would yield more favorable results).

119

APPENDICES

APPENDIX A

Logarithmic Amplifier

A logarithmic amplifier (log amp) results from the placement of

a diode in the feedback loop of astandard op amp circuit [Al]. Such a
log amp is illustrated in Figure A1 and will be analyzed in this

 

 

 

 

 

 

 

 

appendix.
'1’ V F ‘
T, .
R
+ —>
1111 — + 4.
Vin

vout
C D

V

 

 

 

Figure A1. Logarithmic Amplifier

The volt-ampere characteristic for the diode can be that of

equation (Al) [A2].

120

121

(A1) IF=IO[e(VF/K) -1]

Where 10 is the diode's reverse saturation current and K is a constant

dependent on the p-n junction of the diode. And if (VF/K) » 1, this

equation can be simplified to the following approximation.

(A2) 1,. 510 JVF’K)

The results of applying the natural logarithm (In) to this
approximation and then solving for V1.- can be seen in equation (A3)

and equation (A4), respectively.

V
(A3) ln(IF) == ln(lo) + (fr)
(A4) VF a K [ ln(IF) - ln(Io] ]

The condition, if (VF/K) » 1, applies to each of the two previous

equations.

The log amp circuit can now be solved by assuming ideal op amp
conditions--where currents into both input terminals are zero amps
and the voltage between the input terminals is zero volts [A3].
Therefore, due to the virtual ground at the amplifier's inverting input,

(A5) Iin = E- and

122

(A6) Vout = " VF

While, due to zero input current at the inverting input, summing

currents here yields equation (A7).

The amplifier's output voltage can be expressed in terms of its

input current: if equation (A6) is compared to equation (A4),
substituting In for IF ,

(A8) vout = - vF = - K [ mum) - ln(Io) ]

Using equation (A8), and the relationship of equation (A5) gives,

(A9) vout = K[ ln(Io) - 14%)]

If (VF/K) = (Vout/K) » 1, and for ideal op amp conditions.

It can then be said that the logarithmic device (of Figure A1)
converts its input voltage Wm) to a voltage (Vout) that is related to the

natural logarithm of the device's input voltage.

APPENDIX B

Switched Capacitor Filters

Switched capacitor filters (SCFs) operate much like RC-filters,
with the switched capacitors (SCs) imitating the resistor
characteristics of an RC-filter. This concept is illustrated through
Figure A2 and Figure A3, which both show second order Butterworth
filters; Figure A2 is a standard RC-filter whose resistors are replaced
by the switched capacitors in Figure A3 [A4]. The remainder of the
appendix will summarize a proof of the equivalence of an SC to a
resistor [A5].

 

 

 

 

 

 

 

 

 

 

Figure A2. Second Order Butterworth Lowpass Filter

123

124

 

 

 

 

 

 

 

 

 

Figure A3. Second Order SC Butterworth Lowpass Filter

A continuous resistor and its parallel SC realization are shown in
Figure A4. The lines denoted by "1" and "2" can be viewed as a node--
wherein any current (or charge) entering or leaving these lines can be
summed to zero using Kirchoff's Law. Also, the switches are to be
operated by a two-phase clock waveform like the one shown in Figure
A5: when the pulse of $1 goes high, the switch labeled 51 will close
and when the clock waveform goes low this switch will then open.
(The same relationships exists between the other clock and switch,
labeled s2.)

It is assumed that the SC network portion of Figure A4 is
inactive-where both switches are open and C is discharged. And, if
V1 and V2 are independent DC voltage sources, that at time to = nT

the two-phase clock is applied (thus operating the switches).

125

 

 

 

 

 

 

 

i Isl 82 I 1
1+L ‘—
I l
+ I |
V1 l I
- I c; I
l l
L F 1
'l I
1 2
il—> R 4—12
0 JVVVV O
+ +
V V
1
0 JD

 

 

 

 

Figure A4. Switched Capacitor as a Resistor

126

high 0 H r11
low , + t - t o

 

 

 

 

l I l l

I I I I I
‘2‘ I I I I I

I I I I I
h‘gh'r I I I I I

I] II I
10W 17 I i I I>t_to

 

O T/ 2 T 3T/ 2 2T 5T/ 2

 

 

 

Figure A5. Two-phase Clock

When the first clock pulse goes high, the first switch (s1) closes
allowing the capacitor to charge to V1 . (The switches have a small

resistance, R. so the capacitor does not charge instantaneously, thus

the RC constant must be less than the pulse width of $1 for complete

charge transference.) When the first switch opens (and prior to the

closing of the second switch) the charge that flowed into C (across
line 1 and in the direction of i1) is equal to equation (A10).

(A10) Q(t0 + T/2) = 0 v1

The second phase period of the clock then occurs: the second

pulse (82) goes high, which closes switch 82 , causing the capacitor to

charge to V2 . The second switch then opens, and the charge that

l 2 7
flowed into C (across line 2 and in the direction of i2) becomes equal

to equation (All).

This is the difference between the charge placed on C by V2 and the
charge placed on C by V1 . (Notice, that the charge flowing past lines
1 and 2 is not equal to the charge on C.)

Similarly, a third phase period occurs--closing 81 and charging C
to V1 . After s1 opens, the charge that flows as a result (across line 1

and in the direction of 11) is equal to equation (A12).

(A12) Q(to+3T/2)=CV1'CV2=C(V1‘V2)

If this pattern were to go on indefinitely, the last two equations
would be repeated indefinitely. (Therefore, the system's steady state
has been reached.) The resistance of the lower portion of Figure A4,
is defined as in equation (A13).

V - V V - V
1 2
Recalling that the voltage sources are DC (constant) voltage sources,
the current flow past a point in a circuit can be described by equation
(A14).

22122

(A14) 1 =

128

The charge flowing past line 1, during a clock phase and in steady
state conditions, is then expressed as Q1 in equation (A15).

t0+3T/2
(A15) I 91: I Ildt
to-I-T

And, since no charge flows across line 1 when the first switch is
closed (i1=0), equation (A15) is legitimate throughout an entire clock

cycle. Thus,

t0+3T/2
t0+ /2

Equation (A17) is the result of relating equation (A12) to equation
(A16), and dividing by T results in equation (A17).

(A17) 960 + 3T/2) = 1, dt

to-I-‘1‘l2

And, given the definition of average current in equation (A18),

to +3T/2

(A18) I1 (average) = 7}:- i1 dt

to+£72

Then, combining equation (A17) and equation (A18), yields equation
(A19).

129

(A19) Q(to + 3T/2) = T x I1 (average)

And, then substituting in the result of equation (A12) gives equation
(A20).

(A20) C (Vl - V2) = T x11 (average)

This equation can be rearranged as shown in equation (A21).

V1 'V2 _ 1
I1 (average) ' C

 

(A21)

And, if both V1 and V2 are constant during the clock period T (then
11(average) = 11 ) and using equation (A13) with equation (A21) gives,

(A22) R =

Olr-l

Now let the clock period read T , so that its clock frequency is
fc (in Hertz). Then,

(A23) R-E-l
-c 47c

This reveals that the resistance equaivalent of the SC parallel network
can be the inverse of its capacitance, multiplied by its clocking
frequency (assuming proper conditions).

An SC, however, is not always a resistor's equivalent when it

130

exists within a circuit which is more complex than that of Figure A4.
This can be illustrated by Figure A7 -- where an op amp filter (see

Figure A6) has its resistor replaced by the parallel SC [A6]. Notice,
that the capacitor charges as the first switch (61) closes and opens.

When the second switch (82) closes, the capacitor's voltage then exists

across the op amp's terminals (the voltage here should ideally be 0 V).
Fortunately, SCs have many realizations (i.e. series, series-parallel and
parallel-series) [A7]. The resistance(s) in a particular RC-filter design
can usually be approximated by combinations of various SC realizations

within a circuit.

131

 

R1 C1

O—W
+ O
4.
vii Vat
C O

 

 

 

Figure A6. A Standard Op Amp Filter

 

 

 

 

 

Figure A7. A Switched Capacitor Filter

 

APPENDIX C

Trimming

There are many devices on the analog board that require

adjustment and trimming for the heart/breath monitor to function

properly. The trimming of the analog board can be obtained by

following the steps listed below. (It is suggested that this section be

used with the design schematics from Section 2.4 .)

9’

>129!»

Do not connect the microwave transceiver until after step 4.
Turn on the board's power supply (or attach battery).

Adjust the potentiometer, R24, until V,mt (see Figure 41) reads
+8.0 V.

’Durn the board's power off (or disconnect the battery).

Attach the microwave transceiver to the board (see Figure 29).
Turn on the board's power supply (or attach battery).

Attach an oscilliscope to the lst stage's voltage input, Vnn (see
Figure 30).

Producing movement at the input to the microwave cavity will
result in an AC voltage registering at the oscilliscope. (If not, the
oscilliscope settings and the transceiver connections should be
adjusted until this is the case.)

Isolate the transceiver input from movements. (V 1111 should not
reveal any AC voltage. If it does, consider further protection of

the transceiver input.)

132

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

l 3 3
Attach an oscilliscope to the lst stage's voltage output, Vlout (see

Figure 30).

Adjust the offset resistor, R3, until the DC voltage for Vlout = 0V
(within a few microvolts).

Verify proper function of the lst stage (G 1:50) by comparing the
range of voltage at its input to that at its output. (The transceiver
must obviously not be isolated for this verification.)

Again, isolate the transceiver input from movements. (This must
be done for the remainder of the trimming unless stated
otherwise.)

Attach an oscilliscope to the log amp's voltage output, LOGout (see
Figure 31).

Vary the offset adjustment resistor, R6, from one extreme to the
other and note the change. (The DC voltage changes should be as
follows: at one extreme, a stable positive /negative voltage (of 250.2
V) becomes unstable (the signal flickers on the scope) and again
becomes stable, but this time at 0 V : the 0V reading too becomes
unstable, and the voltage procedes to register as an unstable
negative/positive voltage (of 2220.2 V), which stablizes at the other
extreme.)

Adjust the offset adjustment resistor so that the log amp's output
voltage registers a stable 0V.

The offset adjustment for the second stage has already been done
in steps 7-1 1 (the dual op amp has just one adjustment).

The TTL clock frequencies should be supplied to both the lowpass

and highpass SCFs (see Figures 34 and 35).
Attach an oscilliscope to the Lowpass SCF's voltage output, LPout

20.
21.

22.

23.

134

(see Figure 34).
Adjust the filter's offset voltage (using R14) until LP,mt = 0 V DC.

Attach an oscilliscope to the Level Shift's voltage output, V30ut

(see Figure 36).
Adjust the filter's offset voltage (using R13) until V30,“ = 1.25 V

DC.
Analog board trimming is completed.

APPENDIX D
Sampling Constraints

Section 1.2-1 had restricted the monitor's design to the
processing of respiratory signals and heart signals which exist within
the frequency ranges of 0.1 Hz to 2.0 Hz and 0.5 Hz to 2.0 Hz,
respectively. Support was given to establish these ranges as exceeding
the normal expectant heart and respiratory rates for human subjects.
These constraints did, however, assist in. the analog board's design;
from a hardware perspective, all components could be chosen to be
capable of processing signals within these frequency ranges.

The algorithm (thus the prograrmner of the algorithm) needs to
be aware of the signals' frequency limitations in order to reduce both
the processing time, and the space in memory that is occupied by the
the data being processed. This appendix will summarize the

relationships between the following: the frequency range of a signal
(f 1 5 f5 f2), the minimum sampling rate required to reproduce the

analog signals in this range (fs), the minimum number of samples

required (N), and their relationship to the minimum processing time
and the memory space needed in calculations using the data.
Shannon's sampling theorem requires that the monitor must (at
least) sample at the Nyquist sampling rate, f8 2 2"‘fn , (where fn is
the highest frequency in the signal), in order to reproduce the
analog's time signal [A8]. So, as the largest signal rate allowed for

both the heart and respiratory signals is 2.0 Hz, the signal processing
algorithms must use a minimum sample rate of 4.0 Hz (or 2 " f2 ). (A

135

136

larger sampling frequency is desired, as the heart and breath signals
carry higher frequency information that may be related to the signal

rate.)

The minimum number of sample points needed can be
determined once the sampling rate is known: as N 2 f5 / F (where
UP is the largest period of a signal and F is the frequency resolution of
a signal's spectrum) [A9]. It is expected that the collection of data

samples, at a sampling rate of f8 (samples per second), for a time

period of l/F (seconds) requires that at least f8 (1/F) samples are

collected. The minimum number of samples required in processing a
breath or heart signal is then 40 samples and 8 samples, respectively.
(Calculated using fs = 4.0 Hz and F = 0.1 Hz for breath processing, and
F = 0.5 Hz for heart processing.)

The number of samples needed for processing will have a direct
effect on the memory space needed and the time required to process
the samples. This is because each sample will usually require storage
prior to processing--with more samples requiring more space.
Assuming equal sampling rates, it will take more time to collect 40
samples than it will to collect 8 samples.

For test purposes, it is desired that the higher frequency details
are. required for processing. Therefore, the sampling rates for use in
the plots will be increased to 32 Hz for breath signals and 64 Hz for
heart signals. A minimum of 320 breath data samples and 128 heart
data samples are then required for sampling an entire (heart or
breath) cycle: however, twice as many samples will be collected to
ensure that the data represents more than one entire heart or breath

cycle. (See Table A1 for a summary of the sampling constraints

137

specified in this appendix.)

Table A1. Sampling Constraints

 

Expected frequency range
Minimum sample rate
Minimum # samples

Minimum time required

Actual sample rate
# samples needed

data collection time

 

 

HEART
0.5-2.0 Hz
4.0 Hz
8 samples

2 seconds

64 Hz
256 samples

4 seconds

 

BREATH
0.1-2.0 Hz
4.0 Hz

40 samples

10 seconds

32 Hz
640 samples

20 seconds

 

 

APPENDIX E

A Recursive Maximum Likelihood Program

The following is the recurSive maximum likelihood estimation
program that was used as described in Section 3.4. This is a BASIC
program and has been adjusted here, so as to remain with in the
margins of the document. Therefore, where a "+" is in the first
column, it is intended for all information to remain on the previous

line of the BASIC program.

1o'fitttfitttttflt.ittttttfifititfifitfilltt¢tt*3.0tttfitttttttttttttit

20 "" SUBROUTINE ISMDL: PERFORMS PARAMETER ESTIMATION
+FOR IMPULSE RESPONSE"

30 "" AND AR/ARMA RANDOM PROCESSES, IE PARAMETRIC
+SPECTRAL ESTIMATION "

40 "' (c)COPYRIGI-1T 1985, 1986 GREG D. HOSHAL

50 ""

60 '* 1. ALL POLE IMPULSE RESPONSE

7O "' 2. POLE/ ZERO IMPULSE RESPONSE

80 "' 3. AR PARAMETER ESTIMATION (NON-RECURSIVE)

90 "' 4. ARMA PARAMETER ESTIMATION(RECURSIVE)

l 00 tttfittfitttttttttttttfittfitfittfitttfititttttttttttttttttttttIII
l 10 OPTION BASE 1 :DEFINT I-P

1 4O MAX=O : IROW=7+NPARAM"2:TP=8‘ATN( 1 l)

150 DIM (8192),A(10),B(10),COR$(4,2),ZP(10, 10),ZP1(10, 10),V(16),
+ZPHI(1 6),ZPSI(16),ZPV(16),ZP2(10, 10),FAC(8),DAT%(8 192)

170 REM"*RECURSIVE ML ARMA PARAMETER ESTIMATION"""
171 KEY(1) ON

173 ON KEY(1) GOSUB 175

174 GOT O 180

175 N=O:RETURN 261

180 SCREEN 1:KEY OFFzCLS

190 LOCATE 1, lzPRINI‘" MICROWAVE VITAL SIGNS MONITOR ":
200 LOCATE 3, l :PRINT'BREATHING RATE ESTIMATION TEST
+PROGRAM";

202 LOCATE 4, 1 :PRINT" ":
220 LOCATE 8, l :PRINT" 1 . Take sampled data for estimation."

*‘Ifilpilg.

1'38

139

230 LOCATE 10,1:PRINT" 2. Retrieve data file for estimation."
240 LOCATE 12,1: PRINT" 3. Begin recursive rate estimation."

250 LOCATE 14,1:PRINT" 4. Exit to system.

260 LOCATE 15, 20: INPUT N .

261 FOR I=15 TO 22:LOCATE I,1:PRINT SPACE$(39)::NEXT I
280 IF N=4 THEN STOP

290 IF N=3 THEN GOSUB 370:GOTO 320' BEGINE ESTIMATION
300 IF N=2 THEN GOSUB 560:GOTO 320' RETRIEVE DATA FILE
310 IF N=1 THEN GOSUB 2000:GOTO 320"“TAKE SAMPLED DATA
320 LOCATE 15,20:PRINT SPACE$(20):GOTO 200

330 GOTO 260'NEX'I‘ INPUT

340 PRINT"HIT ANY KEY TO BEGIN ESTIMATION"

350 X$=INKEY$:IF X$="" THEN 350

360 CLS

370 NA=3:NC=3'NA=#POLES,NC=#ZEROES

380 SCALE=.99' PREFILTER SCALE FACTOR

390 ZLAMO=.95' LAMBDA ZERO

400 ZLAM=.99' IAMBDA ZERO

410 ALPHA=1' PREFILTER SCALE FACTOR

420 NREPS=1' NUMBER OF TRIALS IN SAME FILE
422 GOT O 660

430

REMfittttiitfitfitfitttttfififittttttttfitttfifitfitfifitttlttttttttttilt

440 REM“*RECURSIVE MAXIMUM LIKELIHOOD ARMA MODEL
+SPECTRAL ESTIMATION‘”

450 REM‘”ALGORITHM. TAKEN FROM IEEE TRINF.THRY.VOL.IT-
+28,NO.4, ”“

460 REM“‘JU LY l 982. “"
470 REM""USER SPECIFIED VARIABLES: “*
480 REM“" AR MODEL ORDER “"“
490 RE1\!1""""I MA MODEL ORDER “*
500 REM"‘ FILESPEC TO FILTER “*
5 10 REM"" FORGETTING FACTOR LAMBDA *"
520 REM"‘ PREFILTER SCALE OR TRANSIENT CONTROL, K“*
530 REM""' (NOTE K=0 ELS; K= 1 MAY BE UNSTABLE *"
540 REM"" UPDATE INTERVAL FOR OUTPUT(NO.SAMPLES) u.
550 REMstssn-taests64688ssoessetaesteatssssstsetstsstasatssst

560 '...*SUDrOUtine to get data file ttfittttitttttlttttttttttttttti
570 LOCATE 18,15:1NPUT'Filespec";F$:LOCATE 18,15:PRIN1‘
+getting file"

580 OPEN F$+".DAT" FOR INPUT AS #1

590 INPUT #1.NS.SR.SOFF,TP$.TP$

600 FOR I=1 TO NS

610 INPUT #1,D(I)

620 NEXT I:LOCATE 18,15:PRINT SPACE$(14);:CLOSE #1

630 LOCATE 18,15:PRIN'1"FILE:";F$+" ":LOCATE 19,15:PRINT"#
+samples= ":NS

640 LOCATE 20,15:PRINT'Sampling rate=":SR;

650 RETURN

140

660 LOCATE 18,15:PRINT SPACE$(14)::LOCATE 19,15:PRINT
+SPACE$(14);

670 LOCATE 20, 15: PRINT SPACE$(14);

680 LOCATE 17,1: PRINT ELAPSED TIME(SCC)":

690 LOCATE l9, 1: PRINT" ------------------- :

695 LOCATE 17,22:PRINT' ESTIMATE ";

700 LOCATE 18,22: PRINT'AVG BRTHS/MINUTE";

701 LOCATE 19, 22: PRINT ---------------- "'

710 FOR I=1 TO NA+NC: FOR J=l TO NA+NC: ZP(I J,)= 0: NEXT J: NEXT I
720 REM‘" INITIALIZE ALL VALUES

730 FOR I=l TO NA+NC

740 ZPHI(I)=0

750 ZPSI(I)=O

760 ZPV(I)=0

770 ZP(I,I)=ALPHA

780 NEXT I

790 ZLANIT=ZLAMO:FOR I=l TO 8:FAC(I)=SCALE"I:NEXT I
800 IDCNT= 1:1PV=NA+NC:ISECCNT= l

810 REM""COMPUTE PREDICTION ERROR

820 'GOSUB 1980' GO DISPLAY UPDATED PARAMTER VALUES AND
+VECTORS

830 SUM=0

840 FOR I=l TO IPV

850 SUM=SUM+ZPHI(I)’ZPV(I)

860 NEXT I

870 EPST=D(IDCNT)-SUM':E(IDCNT)=EPST

880 REM“"UPDATE COVARIANCE MATRIX ESTIMATE

8902 FOR I=1 TO IPV:V(I)=0:NEXT I:SUM=0

900 FOR I=1 TO IPV

910 FOR J=1 TO IPV

920 V(I)=V(I)+ZPSI(J)*ZP(J,I)
930 NEXT J
940 NEXT I

950 FOR I=1 TO IPV

960 SUM=SUM+V(I)"‘ZPSI(I)

970 NEXT I

980 DEN:1/(ZLAMT+SUM)"'”“""MAY BE WRONG ON
+1NTERPRETATION”“"““

990 FOR I=1 TO IPV:V(I)=0:NEXT I:SUM=0
1000 FOR IR=1 TO IPV

1010 FOR IC=1 TO IPV

1020 V(IR)=V(IR)+ZP(IR,IC)‘ZPSI(IC)
1030 NEXT IC

1040 NEXT IR

1050 FOR IR=1 TO IPV

1060 FOR IC=1 TO IPV

1070 ZPl(IR,IC)=V(IR)‘ZPSI(IC)

1080 NEXT IC

1090 NEXT IR

141

1100 FOR IR=1 TO IPV
1110 FOR IC=1 TO IPV

1 120 SUM=0

1 130 FOR K=l TO IPV

1 1 40 SUM=SUM+ZP1(IR,K)*ZP(K,IC)
1 150 NEXT K

1 l 60 ZP2(IR,IC) =SUM‘DEN

1 170 NEXT IC

1180 NEXT IR

1190 FOR 1:] TO IPV

1200 FOR J=1 TO IPV

1210 ZP(I,J)=(ZP(I,J)-ZP2(I,J))IZLAMT

1220 NEXT J

1230 NEXT I

1240 REM

1250 REM“*UPDATE PARAMTER VECTOR”"‘"*""****"'*"'*"'***
1260 REM

1270 FOR IR=1 TO IPV

1280 SUM=0

1290 FOR IC=1 TO IPV

1300 SUM=SUM+ZP(IR,IC)*ZPSI(IC)

1310 NEXT IC

1320 V(IR)=SUM*EPST

1330 NEXT IR

1340 FOR I=l TO IPV

1350 ZPV(I)=ZPV(I)+V(I)

1360 NEXT I

1370 "““COMPUTE CURRENT BREATHING FREQUENCY AND
+DISPLAY‘"

1382 IF ISECCNT<SR THEN 1484 ELSE ISECCNT =0

1400 A1=ZPV(2)-ZPV(1)"'ZPV(1)/ 3

1410 B1=(2‘(ZPV(1)"3)-9*ZPV(l)‘ZPV(2)+27*ZPV(3))/27

1 420 ROOT=B 1 *B l / 4+(Al A3) /27:ROOT=SQR(ABS(ROOT))

1430 AROOT=(-B 1 /2+ROOT) :A=((ABS(AROOT))"( 1 /3))"'SGN(AROOT)
1440 BROOT=(B l /2+ROOT) :B=((ABS(BROOT))" ( 1 /3))*SGN(-BROOT)
l 450 ZR=- (A+B) / 2-ZPV ( 1) / 3 :ZI=SQR(3)‘(A-B) / 2

1460 IF ZR=0 THEN FB=SR/4:GOTO 1482

1470 FB=ABS(ATN(ZI/ZR)"'SR/TP)~

1482 LOCATE 20,3:PRINT USING "#####";INT(IDCNT/SR)

1483 LOCATE 20,23zPRINT USING "#####.##";FB*60;

1484 LOCATE 22,1:PRINT "ITERATION":IDCNT:

1490 REM...COMPUTE RESIDUAL ERRORifitfilllttttttt##‘tfitttfi
1492 ISECCNT=ISECCNT+1

1500 SUM=0

1510 FOR I=1 TO IPV

1520 SUM=SUM+ZPHI(I) l'ZP'VU)

1530 NEXT 1

1540 ET=D(IDCNT)-SUM

1550 REM""UPDATE FORGETTING FACTOR""*"‘"""""""

142

1560 ZLAMT=ZIAMT*ZLAM+1-ZLAM

1570 REM“"UPDATE PHI VECTOR WITH CURRENT D,ET VALUES
1580 FOR I=NA TO 2 STEP -1

1 590 ZPHI(1)=ZPHI(I- 1)

1600 NEXT 1

1610 ZPHI(1)=-D(IDCNT)

1620 FOR I=IPV TO NA+2 STEP -1

1 630 ZPHI(1)=ZPHI(I- 1)

1640 NEXT I

1650 ZPHI(NA+1)=ET

1660 'REM"*COMPUTE FILTERED D AND ET

1670 SUM1=0:SUM2=0

1680 FOR I=1 TO NC

1690 SUMl=SUM1-FAC(I)*ZPV(NA+I)*ZPSI(I)

1 700 SUM2=SUM2+FAC (I)“ZPV(NA+I) *ZPSI (NA+I)

1710 NEXT 1

1720 FOR I=NA TO 2 STEP -1

1 730 ZPSI(I)=ZPSI(I- 1)

1740 NEXT I:ZPSI(l)=-D(IDCNT)+SUM1

1750 FOR I=IPV TO NA+2 STEP -1

1 760 ZPSI(I)=ZPSI(I- 1)

1770 NEXT I:ZPSI(NA+1)=ET-SUM2

l 780 IDCNT=IDCNT+ 1:1NTERVAL=INTERVAL+ 1

1790 IF IDCNT<=NS THEN GOTO 810

1800 RETURN "“‘RETURN TO MENU

2000 REM"*ANALOG TO DIGITAL(ADC): DEVELOPED AND CODED
+BY G.D. HOSHAL ““

2010 REM“"COPYRIGHT @MAY 20, 1985. G.D.HOSHAL,
+E.LANSING,MI ‘"

2020 REM“*“DECODE PARAMETER MATRIC AND COMPUTE
+TIME SERIES““"

2022 LOCATE 16,15:INPUT"# samples":INS:LOCATE
+16,15:1NPUT'FILESPEC":FS$:LOCATE 16.15:PRINT"Any key to
+sample"

2023 X$=INKEY$z IF X$="" THEN 2023

2024 LOCATE 16,15:PRINT" .sampling

2030 NCHAN=1' SET NUMBER OF CHANNELS

2040 ISR=48' SET SAMPLING RATE

2070 REM “"“"““”"”“”cheap a/d program prototype vers 0
2080 REM DEF SEG=7936:BLOAD"B:pclab",0

2090 REM SETUP.ADC = 9 : ADC.SERIES = 12 : SET.CLOCK.DIVIDER
+= 45

2100 TIMING.SOURCE%=0:START.CHAN%=0:END.CHAN%=NCHAN-
+1:GAIN%=1

2110 CRLF$=CHR$(10)+CHR$(13)

2120 NUMBER.OF.TICKS% = INT(800000!/ISR)':GOTO 2152

2130 CALL SET.CLOCK.DIVIDER (NUMBER.OF.TICKS%)

2140 CALL SETUP.ADC
+(TIMING.SOURCE%,START.CHAN%,END.CHAN%,GAIN%)

143

2150 ISAM=INS:CALL ADC.SERIES (ISAM,DAT%(1))

2152 LOCATE 16,15:PRINT SPACE$I14);

2160 '$*#*REMOVE MEAN AND NORMALIZEI‘tttttttfifitittt*****
2161 FOR I=1 TO INS

2 1 62 D(I) =DAT°/0(I)

2163 NEXT I

2170 SMEAN=0

2180 FOR I=1 TO INS

2 1 90 SMEAN=SMEAN+D(I)

2200 NEXT I

22 1 0 SMEAN=SMEANIINSzSUM2=0

2220 FOR I=l TO INS

2230 D(I)=D(I)-SMEAN

2240 SUM2=SUM2+D(I)*D(I)

2250 NEXT I:SUM2=SUM2/INS:SUM2=SQR(SUM2):IF SUM2=0
+THEN SUM2=1

2252 OPEN FS$+".dat"F OR OUTPUT AS #1

2253 WRITE #1,INS,ISR,0,"T ","R "

2260 FOR I=l TO INS'""NORMALIZE TO UNIT VARIANCE
2270 D(I)=D(I)/SUM2:WRITE #1,D(I)

2280 NEXT I:CLOSE #1

2290 NS=INS:SR=12:RETURN

LIST OF REFERENCES

[1] GD Hoshal, M. Siegel, andR. Zapp, r w v H ni r
(Proc. 6th Annual Conf. IEEE EMBS,

1984), pp. 331- 333.

[2] GD. Hoshal, S. Ivkovich, M. Siegel, and R. Zapp, Remote
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WW (Proc. IEEE Conf- Computers in
Cardiology. 1984). pp. 409-412.

[3] EE .11]! {no.1 1 La f 1 __l -. an! E1 0 I Trm ,
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[4] MW, Stan Gibilisco, editor-in-chief, 1st
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[5] The Lippencott Manna of Nureing Preetiee, 4th ed.
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[6] Athanasios Papoulis, r A
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[7] Jacob Millrnan, Microeleetrenics: Digit_2_11 and Analog Qireuits
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[8] Benjamin C. Kuo. W (New York: Holt,
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[9] David A. Hodges and Horace G. Jackson, Analysis and Deeign ef
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[10] Jacob Millrnan, op. cit., pp. 600-601.
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[A4]

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Martin S. Roden, Digital mg Date Qemmunicagen Mteme
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Benjamin Friedlander, A Reeureive Magmum Likeliheed
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Benjamin Friedlander, System Identification Techniques for
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David E. Johnson, John L. Hilbum and Johnny R. Johnson, op.
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1 4 7
[A8] Martin S. Roden, op. cit., pp. 80-87.

[A9] William D. Stanley, Gary R. Dougherty and Ray
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"lllllllllllllll