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The application of an adaptive least squares lattice filter in
the detection of heartbeat occurrences in measurements from
a remote microwave vital life signs monitor

Mahoney, Patricia Ann, M.S.
Michigan State University. 1989

C3

a
it
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313/761-4700 soc/5210600

THE APPLICATION OF AN ADAPTIVE LEAST SQUARES LATTICE FILTER IN
THE DETECTION OF HEARTREAT OCCURRENCES IN
MEASUREMENTS FROM A REMOTE MICROWAVE VITAL LIFE SIGNS MONITOR
By

Patricia Ann Mahoney

A THESIS

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

MASTER OF SCIENCE

Department of Elecm‘cal Engineering

1989

ABSTRACT
THE APPLICATION OF AN ADAPTIVE LEAST SQUARES LATTICE Fn.TER IN
THE DETECTION OF HEARTDEAT OCCURRENCES IN
MEASUREMENTS FROM A REMOTE MICROWAVE VITAL LIFE SIGNS MONITOR
By

Patricia Ann Mahoney

A portable remore microwave vital life signs monitor has been built. Heart rate is estimated
by detecung Doppler shifts of a microwave signal that illuminates the chest wall of a human. A
method of detecring heartbeats is based on modeling the microwave heartbeat signal as the output
of an all-pole filter that has been excited by a pseudo-periodic impulse train. An adaptive least
squares lattice filter is used.

The use of this detection method for a modified version of the monitor is verified in this
research Estimates of the coefficients of the all-pole filter are found. The detection method
works well for only a limited set of operating conditions of the modified monitor. The results of
the verification process suggest an alternative heartbeat detection method could be based on the

detection of changes in the statistics of the microwave heartbeat signal.

ACKNOWLEDGMENTS

The author wishes to thmlt Betsy Mates-Needham and Michael Francois for all of their
help. She is especially grateful to Betsy Mates-Nadham for her help in the development of the

computer program in Appendix J.

TABLE OF CONTENTS

List of Tables
List of Figures

 

 

Introduction
Research Objectives
Verification Method and the Method Used to Estimate the All-Pole Filter Coefficients

 

 

 

Results
Heartbeat Detection with the Likelihood Variable
Conclusions
Recommendations

 

 

 

 

Appendix A: Samples of Files form the Data Base
Appendix 8: Prediction Error Variances Used to Determine All-Pole Filter Order ......
Appendix C: All-Pole Filter Coefficients
Appendix D: The Results of Tluesholding the likelihood Variable Sequence as a
Heartbeat Detecuon Method
Appendix B: We Unnormalized Pie-Windowed Least Squares Lattice Filter Parame-
ter Update Algorithm
Appendix F: Computing the All-Pole Filter Coefficients from the Unnormalized Lat-
tice Parameters

 

 

 

 

 

Appendix G: A Fortran Implementation of the Unnormalized Pie-Windowed Least
Squares Lattice Filter
Appendix H: A Fortran Implementation of the All-Pole Filter Coefficient Update
Algorithm
Appendix I: The Normalized Pre-Windowed Least Squares Lattice Filter ...... ............
Appendix J: A Fortran Implementation of the Normalized Pie-Windowed Least

Squares Lattice Filter
Appendix K: Review of the Development of the Microwave Vital Life Signs Moni-
tor
Appendix L: Review of the Relationship Between Autoregressive Process Synthesis
and Adaptive Linear Prediction

Appendix M: Illustrating the Use of Adaptive Linear Prediction to Extract Impulse:
from Processes Using Speech Processes as an Example

 

 

 

 

 

 

Vii

21

81323

37 '
42
46
4s

51

59
63

87

93

Appendix N: The Unnormaliaed Pre-Wutdowed Least Squares Lattice Filter ................... 98

References 106

 

LIST OF TABLES

Table Bl. Prediction error variances used to determine all-pole film order. ................... 43

 

Table Cl. All-pole filter coefficients. , 45

TableDI. flierestmsofduesholdingmelikelihoodvariahlesequenceasamedtod
ofdetectingheartheats. 47

LIST OF FIGURES

Figure 1. AR model all-pole filter coefficient A, for a chest wall microwave signal.

 

Figure2. ARmodelall-polefiltercoeffieientAgforachestwallmicrowavesignaL

 

Figure 3. AR model all-pole filter coefficient A, for a chest wall microwave signal.

 

Figure 4. AR model all-pole filter coefficient A. for a chest wall microwave signal.

 

 

Figures. ‘I‘heeffectoflonthelikelihoodvariahle.
Figure 6. ‘l'heeffectoflonths predictionerrorsequence.example l. -.........................
Figure7. Wefi‘ectoflcnthepredictionenorsequencemxamplez. ........ ............

Flgure8. Pole-umplotsoftheARmodelan-polefiltersforthehtnnansuhjectfiles
andtheinanimateohjectfiles.
Figure 9. Amplitude frequency respome AR model all-pole filter forthe humm sub-
jectfilesandtheinanimateohjeetfiles.
Figure 10. Recoveredexcitationprocessforachestwallfilerecordedunderideal
conditions.
Figure 11. Recoveredexcitationproceasforachestwallfilerecordedundermore
realisticconditions.
Figure 12. A chestwall fileexample of thresholdingthe likelihoodvariahle. .................
FigureIB. Alegfileexampleofthresholdingthelikelihoodvariable.

 

 

 

 

 

Figure AI. Chestwall filewithhumansubjectatrestandholdinghreath. ......................
FigureAZ. Chestwallfilewithhtunansubjectatrestandhreathing.
Figure A3. Greetwallfilewithhumanmbjectexereisedandholdingbreath. .................
FigureA4. Orestwallfilewithlmmansuhjectexercisedandhreathing. ..............
FigureAS. Legfileofahummsuhjeet.
FigureAfi. Inanimateohjectfiles.

 

 

 

Figure Kl. The first Michigan State University microwave vital life signs monitor.

 

Figure K2. The modified Michigan State University microwave vital life signs moni-
tor. -

 

12

13

14

15
16
18
19

23

883’

38
38

39

41

74

85

Figure Ml. Block diagram of simplified model for speech production. ...........................

Figure M2. Deconvolution of the impulse response of an all-pole filter by linear

 

prediction.

Figure N1. Direct realization of an order M lean squares linear predictor. .....................
Figure N2. Lattice realization of an order M least squares linear predictor. ....................

Figure N3. Characteroftheleastsquareslauice filterexponentialwindowforvari-
ous values of A.

 

99
1(1)

103

INTRODUCTION

mummmdevebpmganmfinvasivevimlfifengmdeteaormawmbeusedby
medicslpersonnelwortinginhanrdmsenvironmems. Onerequirementoftheimtrumentisthat
itisahletomeanrreahtunsn’sheanrateatdimsupmfimchesfiomthehodyandthrough
promedveelothing. Aportahlelowenergymierowsvedevicehasheendevelopedmmeasure
heanratebydetecdngpermhadcnsofdiechestwanduemdtehesrtbestlng. ‘I'hedevice
operamhyilluminadngthechestwaflwithapulndX-hsndmicrowsvesignal Relativemotion
hetweendndevicemddzdteawanudemaedhybopflershifumdnmfieemdmiaowave
signal. Under realistic operating conditions. breathing. body. and background movements
ohscuretheheartheatsignal. Ibeamuuchanengeismdevelopareel-fimesignalprmirrg
teehniquethatwinemactheanheatinformadonfiomthemiaowaverentms.

Panefi‘ommmunuehemmefinmdnmiuowavesignalhaveusedvuiousdmemdfm-
qrmcydomaindemcfionmedndsfiynn.fiym.2app.&$iegd.l986;Byme&SiegeL 1985;
Byrne. Zapp,Flyrm.&Siegel. 1985:}loshalekovich. SiegeL&Zapp.l984:I-Icshal&8iegel.
1985;Hoshal.8iegel.&2app.1984;13n.Kiernicld.Kiemicki,&Wollschlaeger. 1979;Pcpovi<:.
Chlm&Uml984).1hehemmesdmafimwchm®esesnhechsdfiedinmtwomups.wch-
mqtesmmmlymepaiodicnmofmelnmmmchmquamnauemptmidmdfyuuivi-
dualhearthestsinordertoestimatehesrtrate. Detecticnmclmiquesthatrelyonthepericdie
nanueofdnheutheusignflhavehadfimiwdmhemseheumeaocmmam
pseudo—periodic. Trmepetiodshetweenheartbeatsaremtalwaysconstam. Amoconelationisan

example of such a technique. Averaging techniques such as autoconelation also perform poorly

intrackinginstantsneouschangesmthcheertrsm.
ummwummmmmmumywmmum
hesnheatsignal. Amierowavelcuthestslgnallooksmewlntlikeanelectroardiogru
(EKG).1heocamuneofaheume¢mdnmiaowavenpnlqrpesnmheimptufiveMnamre
Peakdetecfioncsnhemedmbescindividualhembemsmmiaowavehembeadgnfls
recordedtmderidealopetatingconditims. mmmmmmm
cmrdifiombecmueuehemngnflisohscmedbydunerdmmhremhhgndbackmd
mmmmrora'mm'mmmmmmmw
unsuccessfiIlMSiegel,personalcommrun'cstion. 1988). 'I‘hesignanrreoftheheertbestchanas
withonemadmmddistanceofthemiaowavedevicewimrespeamthechestwan. margin.
mmcenvaryfiompersonmpmsonandfiomhesrtbemmheumeatmymeaflegele
mexuacdmofmimpulsivengnalfiomaproeeaesisaboaprouemmgeophysiamd
speeehanalysis. Adaptivelinesrpredictionisausefirltechniqueinrecoveriruimpulse
mumbomseianicnacumdspeecthJfithleetMorfilm
Makhoul.l97$). Beemseofmesimflantybetwemdrehnpulsivenauueofhesnbemocamences
inthemicrowavesignalandpitchpflsuhspeedrprmBynreandSlegelOMadopeda
micmwmheumeasigmlmoddmdheanhendaecdmwchmquemnmdmflflmdnspeech
pmcessmoddmdpimhpukedewaorpresmdmleemdmfl(l980).1hedemcdonmemods
arebasedonadaptivelinearprediction. TheparticularpredicmrusedhyByrneandSiegelwasan
adaptive least squares lauice filter. a computationally efficient Implementation of an adaptive
leastsquareslinearpredictor. BymesndSiegelshowedthattheadaptiveiesstsquareslattice
mmwrkedwenmemaedngheanbeamfiommiaowavengnflsmeordedtmdaidalmd

adverse operating conditions.

Byme and Siegel (1985) worked with the Michigan State University Biomedical Signal

Processing Laboratory vital life signs monitor. Other work related to this monitor was done by

BynmflymlappJndSiegKlmxBymebpnFlymmdSiegel(1985).HoslnL1VkDVich.
Siegel. andZIpp(1984).Hoshal and Siegel(l986)andiloshal.8iege1.and2app(l984). A
mprehaniwhinoryofdndevdoprnauofahanumesdmadmmcmfiqumthemchigm
vamvasityvinlnfenpumonhmlsgivenmAppmdixKAmherormodifianmhave
becnmatbmthedesignofmevitfllifesigmmonimrsimednBymuflSiegel(l985):tudy.
namedificsdmswuemademimpmveunufayofmedevicemhumiupowcmmpdon.
hmasednmodmr'sdymmicrmgemdsmnfivity.mdmmrom§gmlcompmxmsreluedm
breathing. Tumuupomonormmmimdmmmemmorummum
changed. mmwmmfimrpodfionprovidesdanthatwmwstmehesnmeesfimaficntecho
niquesunderdevelopmemmoreextensively.
mmaowwefignahmcordedfiomdremodifiedmiaowaveuutappeumhevaydif-
faunfiomflnmiaowmdmkmahymemdSiegdamwmmdndevmof
www.1hewpocofmismkmvedfymnthe3ymmd8bgdmcdd
mdmeuseofmeBymemdSlegdheanheudetecmruevdidfmdumiaowavehanheudg—
nalsreeordedt‘romthemodifiedmcnimr. 'I'headaptlveiesstsquareslatticefilterusedinthe
ByunmdSiegelhesnheudcmaorhapanmetersmamuabedefinedheforedndemcdon
teelmiquecsnheused. BymeandSiegeldidnotgivessysmsdcmedrodofseiecdngvalnesfor
dehmcemmrwdefimdpuammmdmbulkofdfismeheflonhmmm
theseleetionofmerdefinedlmicefilmparametervalues. Abyprnductofthisverificstionpro—
mamummemmmmumormmmmm

ticsctthemlcrowaveheartheasignal.

RESEARCHOIJECI'IVES

mmomwwormmmunmnmmsmusmam
modelsndleanbeaderedonmahodanvafidformlaomheumeangmhmdedfiom
themodifiedvitallifesignsmonitor. BymeandSiegelmodelstlnmicrowavehesrtheusignalas
theoutputofanall-pole filterthatisexcitedbyaproeesscomisdngcfapseudo—periodlcimpulse
u'ainaddedmband-limitedwhitenoise. Equationlistheu'ansferfunctimofdnallpolefilter.

Hui-phyao(z)- T . (1)
1+ An"

whereMistheorderofthefilterandArisacoefficientofthefilter. Tlnlmpulsetralnrepreserus
theoriginalheartbeatsignal. ‘lheall-polefilterrerxesentsthesystemthehesrtbemsignalpasses
through. Adapdvelheupmdicfioncmheusedmdecmrvolvetheompmofman-polefihermat
hasbeenexcitedbyawhiteprocessoranimpulsen-ainwriedlander.198I;Friedlander.l982b:
Lee&Morf.l980:Malthoul.l975). Theexcitaticnpromssismoverahlefiomthsp'edicticn
errorsequence. Adapdvelinearpredicdcnesnalsoheusedmidenfifythecoefficiennofthean-
polefinu.Asmmmgdmadapnvefimupmdicnonwinmvasednopuadmofman-pdefilm
onaprocessconsistingofanimpulsetrainaddedtowhitenoise.BynnandSiegelapplysadq>-
uvefimarpmdicdonmmemicmwaveheanbemsignalmOMermmcovermehesrmea
occurrences from the linear prediction residuals. ‘Ihe heartbeat signal should appear as a

sequence of large predicrion errors.

TheByrnemdSiegd(l985)moddisverysimilumdremrmregremlve(AR)prm
model. Fordrehaufitofmemfsminureader.AppmdingivesarevlewoftheARmeddand
«mammmmmwmdmwmmmoru
BymemdSbgdmoddfwdnmlaowavelnmbemngnuwasmodvuedhyrlnspeeehproceu
modelusedbyleemdMorf(l980)inthdrdevdopmauofapitdrprdsedetector. AppendixM
gimashnplifiedihnfiafimofdnmeoflhearpedlcfimmdtmflysuofspeechmmr
thehenefitofdretmfamiliarreader.

BymmdSbgelflQBSMsumadapdvebstsquueslatficefiherudmflnesrpmdiaorin
thelrhesrtheatdetectionteetmique. municefiherisanormalmdversionofmedreleast
sqummmmusedbyleeandefllmmmdcemchupdneflMMk
recursive.

Alldcemmrpuametercdbddrelikehhoodvuiahlesidsmmeidauificsdmeflnge
mmmmmmmmmmmmmumnu
bg-likefllmodfmfimofflnmmukmmdnhniceflm.mukflmoodvuiahbhs
memeofdnfikdihoodmunmsmedmmpleswincomefiommesmemdisui-
mauaw.rm.mmuwmmuamawmmmcorueww
edness'ofthemcstrecentinputdatapointsmiedlander. 1982a). Afimctionofthellkelihood
mummmmmWWMmmmmmmm
mablesurelatticefiltertoquicklyadapttounexpecteddataaeedtMorf. 1980). Bymeand
Siegelfmndmmdnnquencefomedbymbnacfingmevflueofunlikelflmdvadauefmdn
previmsfimenepfiommeauruulikemmodvadabhvfluecmndbeusedmlsomdnluge
mmmmwmmmmmummmm-
encesequenceisusedmmukoutpmdicdmaromthaannotassodatedfimhesrmeu

occurrences.

mfimnepofmeBymcmdSlegeHwSfihemheadeteedmmismpsssme
micmwwelwanheungnfldlmghmemcemm.mlfltefimvamhkdflermnqm
isformed. mpredicdcnmrmquareemdthcllkemmodvuiahletfimaencesemsm
muldpfiedmgemerJheremhhanquamsofhdnedlugepredicdmummeor
sihleheartheats. mmmwormmuromrrymmmu
micmwaveheanhestsimsfiomdnmodlfiedmcsnheexuaaedwlmmeBymmd
Siegelproeedure. firefirstsrepofdreverificadonproeesswinbetoapplydrelauicefiherto
mmmmnmmmumaawmwummummau
predictionenornquenceandthelikelihoodvariablesequence.

ByrnemdSiegd(l98$)didmtinvesdgamthebehsvimdflnmnfigmfiQOIGnan-pok
mmmMerWQMmmWMMNm-pdemmm
migmconnmmformadmdnthusefidmdndevdmofsheanmmm
MWobjewwormmummmmormm-pbmu
observehowthcyhehaveintime.

VERIFICATION METHOD AND THE METHOD USED TO ESTIMATE
THE ALL-POLE FILTER COEFFICIENTS

The Lattice Filter Parameter Update Algorithm

The Unnormalized Pre-Windowed Least Squares Lattice Filter from Friedlander (1982a. pp.
842-844) was used in the verification of the Byme and Siegel (1985) heartbeat detection method
for the microwave heartbeat signals recorded from the modified monitor. The prediction error
and theiikelihood variable aredirectly available from thelattice filterparameterupdate algo-
rithm. The lattice filter par-meter update algorithm and a Font-an implementation of the lattice
filter are given in Appendix B and Appendix G. respectively. For those who are unfamiliar with
least squares linear prediction and the lattice form, we Appendix L and Appendix N. The all-
pole filtercoefficientestimateswereohtainedfromthelattice filterparametersrhroughanalgo—
rithm given by Friedlander (1982a. pp. 845). The algorithm used to estimate the albpole filter
coefficients is given in Appendix F. Apperrdlx l-l gives a Fern-an implementation of the algoritlun

used to estimate the all-pole filter coefficients.

The Data Base of Files Recorded from the Modified Monitor

The verification process was facilitated by the formation of a data base of microwave sig-

nals recorded for various operating conditions of the modified microwave vital life signs monitor.

SamplesoffilesfromthedatabasearegiveninAppendixA. Therearelo24datasamplesin
eachdatafile. 'I'hesamplingratewasasamplespersecond. Microwavesignalswererecorded
fortwoltindsofrellectivesurfaces.human subjectsmdinanimate objects. ‘Iheinanimare objects

consistedofawoolsurface.ametalsurface.andanopenroom.

muuexpenmemsmponedmuusreseamhtlrerewerefourhumanmbjeets. Foreach
human subject five microwave signals were recorded. Four of the five signals resulted from
reflecting a microwave signal off the chest wall of the subject. The fifth recorded signal resulted
from reliecfing the microwave signal off one of the subject’s legs. Each subject was rested and
holding hismerbreath forthe firstchestwall file. The subjects were restingarrd breathingnor-
mally forthesecondchestwall file. Inthethird file.thesubjeetshadbeenexereisingandhcld

their breath. The subjecrs were exercised and breathing forthe fourth chest wall file.

Themmutorhaduresameponuonwimrespectmdrembjeaforeachcheuwanfile. The
subjeCts were seated. The monitor was pointed just left of center of the chest wall. Studies previ-
ousto this mseamhshowedmnunnmngestheanbeatsignalscanbefomrdinmicmwwesignfls
recorded with the monitor positioned left of center of the chest wall (M. Siegel. personal com-
munication. I988). The monitor was place about 6 inches from the subject. The subjecrs were

wearing Street clothes.

Heartbeat reference signals were obtained from an in-house designed unit that measures
hodysurfacepotentialbetweenthehandsofahumansubject. Theoutputofthedeviceresemhles
anEKGsignal. Ahandpotauialmfemnceheartbeusignalwassimulmreouflymcordedforeach
chestwall file.

A microwave signal reflected from the bare calf of a leg of each subject was recorded. The
monitor was positioned 6 inches from the leg. A hand potential reference heartbeat signal was
simultaneously recorded. Movement detected in the returns of the microwave signal from the leg

due to the heart heating is expected to be insignificant.

 

The data base includes three files where the microwave signals were reflected from the inert.
imate objects. One microwave file was recorded for a microwave signal reflected from a wool
surface placed 6 inches from the monitor. The second file resulted from microwave reflections
fromafiatmetalsurfaceplacedoinchesfromthemonitor. ‘Drethird fileisarecordofreturrn

from amicrowavesignalsentintoanopenroom.

The Selection of Lattice Order

'I'heproperorderof the lattice filtermustbechosen beforetheverification of the Bymeand
Siegel (1985)deandhcartbeatdetecticnmethodforthemodifiedmonitorcanproeeed. The
orderoftheall-polefilterintheBymeandSiegelmodelwillbetheaameastheproperorderof
thelatticefilter. firemeurodusedtodetermhrethepTOperorderofdrelauicefilterisbasedon
tlnoptimizationcriterionofleastsquhreslinearprediction. lnlinearpredictionthecunentvalus
ofaproceesisesfimatedbyafinearcombinationofpastvaluesofmepmcessThecoeffieients
inthelirrearcombinationarechosensuchthatthesumofthesquaredpredictionerrorsisminim-
ized. meperorderofthefinearpndiaoristhemtmberofpastdandemenumtheumu
combination. lftheorderoftheleasrsquaresllnearpredictorisgreaterthantheorderofthepro—
(mathslinearpredictorisusingpastdatainitspredicrionofthecurrentdatapointthatthe
mnemdaupoimismtdependemmtmgwsspmpmcessdedmtmakeamm
tributiontothepredictionofthecunentdataitem.Theweightthelinearpredictorassignstothe
excessprocesselcmerusshouldheclosetozero. Iftheexcessproceeselemenrsmalteonlya
smallconnihufionwunpredicfionofmemnuupocessdunnmmuremcfmesquamd
error shouldnotsignificantly change withanincrease inlinear predicricnorderbeyond theorder

of the process (Chandra 8: Lin. 1974). The order of the microwave heartbeat signals was

10

detenninedbyprocessingthesignalswithahighorderlattice filterandthencalculatingthcmean
ofthesumofthesquaredpredictionenorsforeachlowerordersectlonofthelatticefilter. The
orderoftheprocesswaschosentobetheorderatwhichthemeanofthesrsnofthcsquaredpred-
ictionmordnvanmofunpredicfionmbegmmhvdofi'forinaeasinglauicefilter
order.
Apreliminarystudywasdorreinordertoestahlisharangefortheorderofthemicrowave
signalsinthedatabase. Datafilesrecordedfromthemicrowavesignalbemgrellecmdfroma
humanchestwall.ahumarrlegandtheinanimateobjectswereprocessedthroughslatticefilterof
order 8. Theexponential weighting factor.aparameterof the latticetobeexplainedintlnnext
section. was arbitrarily setto0.95. Thevariance ofthe predicrion error leveledoifatordeu for

each data file.

Inansumequaumalysesoffilesfiommedatabaseahuicefiherofader6wasuse¢
The exponential weighting factorwas setto 0.99 for reasons giveninthenextsection. ‘Ihevui-
ance of the predicricn errors for order I through 6 were recorded foreach file inthe data base.
'I‘heresultsaretabulatedinAppendixB. TheresultsinAppendixBarethesameasthcresultsof
thepreliminarystudy. ‘l'hcvarianceofthesumofthesquaredpredictionenorsforeschfilein

the data base appears to level off at order 4.

The Selection of a Value for the Exponential Weighting Factor, A

A secondparameterofthe lattice filterthatneedstobedefinedbeforethelattice filtercan
he used is the exponential weighting factor. L The exponential weighting factor determines the
configuration of exponential window that weights the past data used in the estimation of the

Statistics of the signal being processed by the lattice filter. As the value of A increased. the length

ll

of the exponential window increases. A study of 1's effect on the lattice filter’s processing of
microwave heartbeat signals wasmade inorderto choseavalue for).

Agroupofchestwallmicrowavesignalsfromthedatabasewereprocessedthroughthelat-
ticefilterwithxsetatvariousvalues. lwassettovaluesrangingfiomo.99too.85. A4thorder
latticewasused. Thehehavlorofdteoutputmdpanmetersofdelatficefilterwasobservedfor
each file. Three consistent behavior patterns were observed. The behavior patterns occurred in
the estimated coefficients of the all-pole filter. the likelihood variable. and the prediction error
sequence.

‘I'hevalueoftheall-polefilterparameterswereupdatedforeverynewdatselementofthe
file beingprocwed. Figure I through Figure4illustrate howthefour all-polefiltercoefficients
varyintimeforl-O.99.1-0.95.and3.-O.90. Forl-O.99.theplotsoftheall-polefilter
coefficients are srnoorh. As ideas... in value. the plots ofthe coefficients showlarge varia-
tions.

FiguresshowshowthelikelihoodvariablehehavesforA-0.99.1a0.95.and).-O.90. As
Adecreasesinvalueuievariaticnofdrelikelihoodvariableirrcreases. Inmostofthechestwall
filesstudied.ariseandfallofthelikelihoodvariablecanbeconelatedwithaheanbeat
occurrencefromthehandpotentialheartbeatreferencesignal. Aldnughthehehavioroftheliltel-
ihood variable reported in Byme and Siegel (1985) is similar. the rise and fall ofthe likelihood
variable associated with theoccurrence of aheartbeatare fasterintheByme and Siegel study.

The rise and fall of the likelihood variable in this research appears to be more like a hump.

The behavior of the prediction error sequences for decreasing values of A was opposite the
behavior of the all-pole filter coefficients and the likelihood variable. As 1. decreases. the ampli-
tude of the largest prediction errors seem to decrease. The variation of the prediction error for
decreasing values of A is m as pronounced as the variations observed in the all-pole filter

coefficients and the likelihood variable. The variance in the prediction error for different values

12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.0-1
(0 "'5‘
.10-
251
r r r l T
2 4 6 2 to
4.0-1
0» "5-
4.0-1
.ud
r r r r r
2 4 6 8 lo
4.01
(c) 4.54
.10-
.25..
f l r I r r
0 2 4 6 8 lo
‘.
- i ' .
(d)0.0- Hi” ’ t ‘. r; ‘ il l
r r l r r
2 4 6 8 to
Time (aeeurds)
Figure l. ARmodel all-pole filtercoeflieientA, forachestwall microwave signal. (am. for

1:099. (b) A. for 1:0.95. (c) A; for 1.1-0.90. (d) chest wall microwave signal.

l3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.0-
(a) 2.0-
1.0-
I I I I I I
0 2 4 6 8 l0
3.0-
(b) 2-0-'
1.0-1
I I I "l I I
0 4 6 8 10
3.0-
(c) 2.0-
1.0
I I T F I I
0 2 4 6 8 10
(d) 0.0.. ‘7 ‘ ~ " -' . I I ’ '.
I I T I I I
0 2 4 6 8 10
Timemccnds)

Figure 2. ARmodel all-pole filtercoefficientA; forachest wallmicrowave signal. (am; for
1:40.99. (b) A 3 for 1:0.95. (c) A; for 150.90. (c) chest wall microwave signal.

16

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0
0.8-
( ) M"
a
00‘-
0.2-
0.0-
I I I I I T
0 2 4 6 I 10
1.0-I
0.8d
(b) 0.6-4
Me
0.2—
0.0-
I I I I T j—
0 2 4 6 8 10
1.0-
0,3-
) 0.6-
(c 0.4...
0,2-
0.0-1
I I I I I I
0 2 4 6 8 10
0.0 I I I I . . l I ' I . I I i 'J l
(d) " . ' : ‘ r‘ . I '
I I I I I I
0 2 4 6 8 10
Time(seccnds)
Figure 5. The effect of 1. on the likelihood variable. (a) likelihood variable with 11-099. (b)
likelihood variable with 1x095. (c) likelihood variable with 1:090. (d) hand poterlial heart-

beatsigml.

l7

ofkisgreaterforsomefilesthanitisforcthers. Figure6andFlgure7shcwtheerrorsequence
fortwodifferentfilesfromthedatabasefilteredwith1-099.1=0.95.and1-O90. Thevari-
anceisgreaterforthepredictionerrorsequenceinFigurefithatitisinFlgure7.

The behaviors of the allopole filter coefficients. the likelihood variable and the predictim
errorsequencecanberelatedtoeachomerbycmrsidefingthelutgthofmeexpmentialweighfing
windowofthelattice filter. Aslincreases.thelengthoftheexponentialwindowittcreases. For
larger values of1. the lattice filter's memory of the process it istrying to predict is longer. More
pastvaluesareusedbythelatticefiltertoestimatethestatisticsoftheprocess.

Thefikelflioodvanablecmbeusedamhtdicamroftheevmudutthemostrecmndan
pointsreceivedbythelatticefilterareoutliersfromtheoauasimdisuibuticnofthedatathatthe
filterhasinitsmemorymeeokorfJQSO). Askdecreasesdhevariancecfthelikeliheodvari-
ableincreasesforthemicrowaveheartbeatsignals. Gertenlly.theperiodsdufingwhichthelikel-
ihoodvariablensesandfallscenelatewithcccunencesofheartbcats. Themicrowaveheartheat
signalappeanwbedifferuumchamerforpenodsmatconelamwimuieocmmuweofhean-
beats. lfthelengthofthememcryofthelatticefilterisshorterthanthetimebetweenheartbeats.
urenuieoccunenceofamiacwaveheanbeatmayappeartobeafarouuierfrcmthedistribution
ofthedatapointsthatjustprecededit. Undammcondtuommevarue ofthelikelihood vari-
able should rise. If the memory of the lattice filtercovers the occunence of several heartbeats.
theoccurrenceofanewheartbeatmaynotappeartobesuchadistantcutlier. Thevalueofthe
likelihood variable would vary less for a lattice filter with a long memory than for a lattice filter
withashortmemory.

The behavior ofthe likelihood variable directly affeCts the estimation ofthe lattice filter
parameters used to calculate the all-pole filter coefficients. A function of the likelihood variable
isusedasagaininthcupdate algorithm forthelattice filterparameters. Thegain enablesthelat-

tice filter to quickly adapt to changes in the process being predicted. If the likelihood variable is

l8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0‘ l ‘ ['1 lI
(a) . I
.20-
.40..
I I I I I I
0 2 4 6 8 10
m-
l I 1 I I ’ 11 t I» i
(b) 0' ‘ ‘ ‘ r I «l ' ‘
.20..
40‘
T T I I I I
0 2 4 6 8 lo
20-
0.! 'l - 'i. g, 7.1 . . I} I l
(e)
-20 _.
4° -
0 2 4 6 8 to
(d) 0—
| T I I I I
o 2 4 6 8 10
Time (seconds)

Figure 6. The effect oflcn the prediction errorsequenee. example 1. (a)errorsequence with
1:099. (b) error sequence with 1:095. (c) error aeqrence with 1:090. (d) hand potential
reference.

19

5:: WWW!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r l I T I T
O 4 6 8 10
50-4
I I I ‘. . I
(b) o d ' . | 1 i 1 'I .' '3‘" 1 ",1 ‘ 1 i I . ' I f '1 I“! '1! I
l .
.50-
T l l l l l
0 2 4 8 10
50.4
(c) 0_ . " t : ', .' if... 3 J; ‘ .
.50-
I l T fi l I
0 2 4 6 8 10
(d) 0.0 — ~ ' " ' l , : ‘ I ’1 ‘ ., l.
l I I l I l
0 2 4 6 8 10
Time (seconds)

Figure 7. The effect of 1. on the prediction errorsequence. example 2. (a) error sequence with
1:0.99. (b) error sequence with 1:095. (c) error sequence with 1:0.90. (d) hand potential
reference.

20

large.menutelanicefilterrespondsbyaneringitspanmetentcminimiaethesumoftheaquared
predictionenors. Theinfonnaficncomainedmuremcstrecuudanpoinnreceivedbythelanice
filterwillbeconsideredtobettetargetmwhichthefilteradapts. lttheparametersofthelafice
filterchange.theestimates of the all-pole filtercoefficientsmightslnwvariations.
mvmadmninmepmdicuonarcrsequencescmbemhmdmthelmgmcfmemanwy
ofthelatticefilter. Whendrememoryofmelanicefilterisahottmedaumelmicefilteristry-
ingtoadapttcislocaliud. Thelikelihocdvariableismoreaaurtivetochangesinthedatathe
latticefilterreceives. lfdrelikelflmodvaflableismomaaoifivemdrmrgeammelauicefiher
isbeuerablemuacksmncrmdnngesmmemicmwavedgnalmchnmiaowavemfiecfim
duringtheoccurrenceofaheartbeat. Ccruequently.thelatticefiltermaybebetterablemminim-
izethesumofthesquaredpredicrionerrors. Thiswouldeaplainwhytleamplitudesofthelarg—
est predicficn errors decrease for decreasing lattice filterexpcnential window length.
ThevaluecfkchosenfortheverificationoftheBymeandSiegel(l985)modelandheart-
beatdetectionmethodwasx-099. Longhnicefiltermemcrywaschcsenbeemaethelarge
predictionenorsassociatedwithheartbeatsinthehandpotential referertcesigmlweremorepro-

nounced. The all-pole coefficient sequences are smooth for 1. a 0.99.

RESULTS

The Byrne and Siegel Model All-Pole Filter Coefficients

Bsdmflesofdteafl-polemtercoefficianswuefoundforeadtfileinflaedaubase. The
afl-polefihercoefficieflestimateswereupdatedfcreachpoiminafile. Ameanvalueofeach
coeffidemforeaehdambaefilewufmmdfiomamfleofconeearfiveesfimaescfde
coefficients. EaehsampleconsimdofmpoimsstartingatpoimMor3nccndsimome
coefficientfile. Thepurpoaeofdredehyinthestmofuresmnplewastomsurethatdrelauice
filmsparameeershadcurverged. AppendixClsatabulaticnbfthe all-polefiltercoefficierrtsam-
pleaveragesforeachfileinthedatabase.

Than-polemwrcoeffidmoffilesformimowaves'mfieaedfimndnmmmbjeasam
closelnvalue. Them-polefiIterccefficientsoffilesformicrowavesrefiectedfrminmumue
objmarecloseinvalue. Themeanofthecoefficientsfcrthehtnnmsubjectfilesandthemean
oftheinanimateobjeetcoefficientsaregiveninAppendixC. Theccefficientsfortheinanimate

object files arelowerinvaluethanthe coefficients forthe human subject files.

lnmdermdetermimlffindiffaencebetweendtehmnhnamobjectmean-polefiher
configmfionmddtehtmutsubjeafilean-polefilmrconfigmaficnissigrfificam. pole-zero plots
weremadeforthetramferfimcticnsoftheall-pole filters forbothfiletypes. Thepcle—aeroplots
areinFigures. Thefourpolsaofeachall-polefilterappearastwoconjugatepairsinthepole-
reroplot. Theplotshowsthatthepolesofthedifferentfiletypesareclose. Figure9aandthure

9b are plots of the amplitude responses of the different file type allopole filters. Although the

 

 

 

HII ' (Z)= 2‘
“M “I“ z‘ - 1.93423 + 2.48522 - 1.6842 + .7273

m...- 05' (z)= 2‘
m" p“ z‘-I.35623+1.68022-1.013z+.s994

Figure 8. Pole-zero plots of the AR model all-pole filters for the human subject files and the
inanimate object files. H - Human subject AR model all-pole filter poles. l - lnartimate object
AR model all-pole filter poles.

 

lS-I

10 -
(a)

H

 

O—I

 

 

 

O.-
5
8
[in
3

 

15-

10—

(b)

 

 

 

 

l l I F l
10 is 20 25 30
Frequency (Hz)

o—
LA

Figure9. Amplitude frequencyresponseARmodelall-pole filterforthe humansubjectfilesand
theinanimateobjectfiles. (a)frequeneyrespomeforthehtunanntbjectfiles. (b)frequency
responsefotheinanimateobjectfilcs.

24

resonancepeaksfortheallopole filterforthehumansubjectfilearegreaerinmagm'nrdetlmthe
mmncepeaksfordefll-pokfihercfdehrflmamobjeafileememcepeabueu

approximately the same frequencies

RecoveryofthafleartbeatSignalftomtheMlerowavefleartheatSlgml

mmwmwdmmwummmunmmwamm
«mamammmvwdmnmmmnmmmm
modified monitor. lftheByrrnandSiegel modelisvalidfcrthetnodifiedmatitormicrowave
heanbeungmhmdfinarprediaimwmmvmseunopaafimofman-pdemmmaprm
consisfingofmimptdsemmaddedmwmmmisenhenthepredicfimenonofmelatfleefilter
shouldcomistofanimpulsen-ainaddedtowhitemise. mimpulsetrainshouldcerrelatemthe

occurrencesofheartbeatsinthehandpotential referencesignal.

Onlyafewchenwaufileshadpmdicfimenorsequencesmaresunbledmhnpulaem
addedtowhitenoise. 'l'hesefilesweremordedtmderidealccnditicns. Thehtnnansubjectwu
atrestandholdingher/hisbreath. 'l'herewaslittlemovementofthechestwallduetou'eathing
orthebodymoving. Figure lOshowstheorigmalmicrowaveheattbeatsignalandthepredictim
errorsequenceforachestwallfilewherethemodeliswellfiued.

Hembeatocmtmmcheawaufilesmcmdedmdermonmdisticcpemingccndificm
arenoteasilydetectablefromthepredictionenormquences. Forfileswherethealbjectswere
bumbing.dcpmdicfimenomubcafiomofhemtbenswmenmdisfingtfisheflefiomodnr
prediction errors. Figure 11 showsanexampleofapredictionerrorsequenceforacl'testwallfile

recorded while the ntbject was breathing and after the subject had exercised

 

 

 

 

 

 

 

 

 

 

 

 

(0 o— w I I I ‘ I ., n _ I
l I I I r T
o 2 4 6 a lo

I I ..
o_ w I I III... ,' I I

(b) ‘ ’ ' ’ ‘ I I'
T— l T I r I
o 2 4 s a to

(d) 04 ' .' '
l l I I l T
o 2 4 s . a to

Tima(aeecnds)

Figure l0. Recoveredexcimfionprocessforadrenwanfilerecmdedmderidealcondifim (a)
chestwallmierowavesiml. (b) predictionenoraequuies. (c) handpotentialheanbeatsignal.

(a)

(b)

(d)

26

 

 

 

 

 

 

 

 

 

 

 

 

 

0- I I V ,
I r T I I I
0 2 4 6 8 l0
l
0" ' I '11 1‘” i ,I
I
T I I I I I
0 2 4 6 8 10
0-1 I I
I I T I I I
0 2 4 6 8 10
Trme(seccntk)

Figurell. Recoveredexdufionpmceufcrachestwanmerecmdedtmdermoreredisficcmdi-
tions. (a)chestwallmicrowavesignal. (b)predictionerrorsequence. (c)handpotentialheart-

beat signal.

27

hmofhrppwabnmnmambemmmmm
handpotcmiallcfmflleisnotcomismforflndwwanm mbehavioromewedthat
mmfimhmomchmwflflemflnmhamhbehnfioroflhefikdflnodvaiaflc
menofthechwwmmmuammpmmelikdihoodvmmmfwmof

mmmmmmnfmfim

HEARTBEAT DETECTION WITH THE LIKELIHOOD VARIABLE

Tlfisseaionpmsunsmemnnuofminvesugauoohtmdnfeesibflltyofdevebpinga
heartbeat detector using only the likelihood variable. Heartbeats were detecwd by applying an
arbitrarythruholdot‘OJtomelikelihood variablesequenceeofallthechestwallmes. lithe
value ofuteukefihmdvanablerunainedumaWOJfor4camrdvepoimafikemmod
variable clusterwas formed. Note thattheliltelihood variablesequenceswerepmduoedbyalat—
tice filterwith 1:0.90. Inordertoverifythata flle'sliltelihoodvariablectusteraequence
representsthe file's heartbeat signal. eachliltelihood variable clusterwasclassifyedas abeartbeat
cluster or a non-heartbeat cluster depending on the location of the cluster in relatiat to the heart-
beats ofthehandetential referencesignalofthefile. Aclusterwaselassifyedasaheartbeat
clusteriftheclusteroccurredduringtheperiodbetweenthereferenceheartbeattothehalfway
pointtothenextreferenceheartbeat. lfaclusteroccurredduringtheperiodbetweenthehalfway
poim andthenextheartbeaLtheclusterwasclassifyedasanon-heartbeat cluster.

The number of heartbeat clusters. the number of non-heartbeat clusters. and the number of
heartbeats in the reference signal were tabulated for each chest wall and leg file from the data
base. Appendix D contains the tabulation of these results. The percentage of reference heartbeats
associated with a likelihood variable cluster was calculated for each tile and was recorded as the
percentage of hits. The percentage of likelihood variable clusters not associated with reference
heartbeats was calculated for each file and was recorded as the percent of false alarms. Figure 12
shows an example of thresholding the likelihood variable sequence {or a chest wall file. Figure

13 shows the result of thresholding the likelihood variable sequence for a leg file.

28

 

 

 

 

 

 

 

 

 

 

 

!
(a) o- ’ . 'I
I l
I T W T I
8 10 12 14 16
0.5-4 , .1
(b) '
I I I I I
a to 12 14 16
n 1 ' n r r . r
(c)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“7L
[
f
E
L
L
L

 

(«11' V" "

 

 

 

I r I I r
8 10 12 14 16
Time (seconds)

Figure 12. Achestwalllileexampleofthresholdingthelikelihoodvariable. (a)chestwall
microwave signal. (b) original likelihood variable sequence. (c) likelihood variable cluster
sequence. (d) hand p0tential heartbeat signal.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(I) o...
I I r I I
8 10 12 l4 16
0.5..
(b)
I I I I I
8 10 l2 l4 l6
1
l r H w
(c)
j I I I r
8 10 l2 l4 16
(d) 0.0-1 ' .. ' .' ' . I ‘ ' I" ,
I I I I I
8 10 l2 14 I6

‘l'lme(seeonds)
Figure 13. A leg tile example of thresholding the likelihood variable. (a) leg microwave signal.
(b) original likelihood variable sequence. (c) likelihood variable cluster sequence. (d) hand
potential heartbeat signal.

31

Fordneeofniedassificatiomofmedtenwanfileamteperwmgeofheanbeau detected
isabout80%andtherateoffalsealarmsisleasthanZO%. ‘1'hresholdingthelikelihoodvariablc
at0.5isfarfrombeinganoptimaldetector. Figure 12showsaectiomofthelikelihoodvariable
sequareemuwemnmidaniaeduheanbanyabysightseunmbeobviousheartbeats
occurrences. ‘l'lie0.5tluesholdmaybetoostringentofarequirement. Althoughsomeheartbeats
werenotdctected.thepefiodicltyofthedeteetedheanbeaucouldbeuwdintheecdmatimof

heart rate through a technique such as autocorrelation.

The percentage of detected heartbeats forthe leg data was low. 50%. The rate of false
alarms forthelegdata. 30%.washigherthenthefalsealarmrateforthechestwalldata. Thelow
heartbeatdetectionrateandthehigherfalsealarmrate forthelegdataindicatesthatlikelihood
variable cluster sequence resulting from thresholding a leg likelihood variable sequence at 0.5
doesnacorrelatewirhthehandpotential referenceheartbeatsignal. Eachlegfllehad 181020
likelihood vafiabledustenwhfledunumberofluanbeminthehandpotendflsignalsvafled
from 35 t020. Theconstantnumber of likelihood variable clusters fortheleg files and the vary-
ingnumbcrsot‘heartbeatsinthereferencet‘tleshelpsmppontheconclusionthatthelikelihood
variableelustersofthelegtileadonotcorrelatetotheheartbeatsinthehandpotential reference

signal

CONCLUSIONS

Theprimuyobjecfiveofdfismsearehwumvaifydmdnflymmdfiegdumw
andlnmbeudewaimmeflmdueappmpdmetormiaomhembeudmflsrecmdedflcm
themodiliedmonitor. TheBymeandSiegelmodelseemstoholdforonlyafewchectwallnlea
hundredaubase.1befileswemrecomwmrderidedcondiuonsfiorhembeum The
subjectswerestillandholdingtheirbreath. Distinctivelargepredictionerrusarecoincidentwith
unmarmmmuemmnmnmmmm Former
mcomedwithmaemovemauoftheeheawammeBymeuxlSlegelmodddoeanuaeunm
holdaswell. htheeefimmepredicdonarouthatarenearheanbeulmuenotdisdn-
guishablefrcmpredicdonencrsbetweenheartbeatoccurrarcee. ‘IheByrneamlSiegelmcdel
maynmsuffidarflydtancmnaememiaomheutbeusignuwhenmemkcheawdlmove-
mentduetoaourceaotherthantheheanbeating.

Whenlinearpredictionisusedtodeconvolveapmitismedthatthegoceasistln
resultofexcitinganallopole filterthathasallofitpolesandzemahsidethemtitcircle. This
impliesthatthesystemslinearpredicuoncanhrverseareminimmn-flme. lfthesystemthe
heanbeasigrdpassamroughkmtmunmum-plimadapdwnmrpmdicdmwmnmuawy
deeonvolvethemicrcwave heartbeat signal. ‘1'hepredictionerroraequencewouldpsobablynot
resemble the original excitation process. If the microwave heartbeat signal is the outptrt of a
non-minimum-phase system. the prediction error sequences resulting from processing the
microwaveheartbeatsignal files recorded whenthesubjectswerebreathing maybeexpected.

1‘)

33

Unearpmdicnmmaynuexacdydecomolvethemicmwaveheutbeusignalevenifdu
minimum-phase all-polemtermodelheldforthemierowaveheartbeatsignal. lftheall-polefllter
headtedbyawhitepmcecmasinglehnmmmmaacflydecmvomw
otnputoftheall-polefllter. Awhlteproceasoraaingleimpulaeareunccnelatedprm Both
proceaaeahavellatspectra. Anlmpulsetrainisconelmed. Thelhrearpredlctlonmaybeblased
braprocmmnmnuhomucidngmmmfllwrwhhamnflaedmtmmm
intonnadonofmeexdmicnprmmaybeabeorbedinmelinearpredlcdon. Thepredictlcn
mmflbemflngoflurmmhprmmmman-polemmnmm
icticnerrorwillbemorewhitethattheoriginalexcitationproceas. lfthemicrowaveheartbeat
sipalcouldbemodeledastheoutputofanan-polefllterexcitedbyanhnptrlseumtheimpulse
uainmaymtbemcovemblefiundnpmdicdonaronbeeuneofimwfladeconvoluflon

man-polemmciamwueobtainmmehopeofgahflngnewmfmmadonnmtmigmlclp
inthedevelopmeruot‘aheartrateestimaticnmclurique. ltwast‘omdthattheconngurationofthe
m-poleflherwaumfmmfwmedanbuefilammbasefilauetherenmofmnecdng
microwavesignalaotfverydifferentsurfacea. Onethingthatallthedatabaseflleahaveincom-
monisthemcnitor. 111eall-polelllterintheByrneandSiegel(l985)modelmaybemodeling
themonitor.

Theflkdflmodvanamewuunmoacmsimsourceofinformadonabomdnlocadmof
heartbeatsinthemicrowavesignalsol’thisdatabase.‘1'hefactthatthelsolationofpedicticn
massodaedwimheartbeanmmenymemdSiegd(l98$)leanbeadeccfimwchuque
mfiamthefikdihoodvafiablesequmcewppommewndusimummefikefilmodvamueisa
goodsotnceofinformafionabomdreloafionofheartbeminunmicmwavesignfla ‘Iheinvee-
tigationimodreuseofdrefikefilnodvafiaflealmeinmedaecdmofheutbeanslmweddmh
maybefun’blewesfimamheanratehcmmelikdflmodvamblesequormedmbm

chestwall tiles. Thelikelihoodvariable ofthelatticefilterisprobablynottheoptimal way or

34

detectingchangeainthestatisticsofastochasticprcwas. Othermethodaofdeaectlngchangeain
drudsfiaofsmdusficprcmsbofldbeccnfidaedbefomamuhodudngmehficeflha
lfltefihoodvanablewdeteaheanbeaninmemiaowaveheanbeudgnabbdevebped
mmmammsmtrmmmmmmm
nabeacceptedmnjecwdfmmeduiahmmedncmdnmdinedmbetuenunfidhy
oftheassumpdonsofthemodelanddetectionteclmiquearehrveatlgamd. UMBymndSlegel
modelisvalid forsigndsrecordedhcmdremodlfledmafimrJtappemsthuthecmfigurafionof
theall-polelllterisunil'ormforthelllesinthedatabas. Theccnsiseubeluviorofthelikeli-
boodvariable forurefileeofthedatabasenrggeaathmlnartbeanmmemmwaveheumeat
slgndcmbeidufifiabhbymedewcnmofchmgummemofmemavehembem

signals.

RECOMMENDATIONS

mnymeandSiegdumHmdymdddsrecuchcasidaedonlympimhpflsedaec-
tor. Becauaeofmesimnantybetweaitheproblemsofflndingpitchptnseainspeech
proceueamddaecdnghemtbeaninuumianwaveheumemdgnflgwnrpitchptflse
mmmummammmormprmmdmamw
mqueamigturevealmommformanmabmnmefimimdonsofusmgnnearpredicnonmd
waystooverccmethoeelimitations. mthodsotherthanllnearpredicticnthmcanbeuaed

todetectheartbeatsfrcmthemicrowavesignalsmaybeformd.

mcuueqmofunnghneupredicuonmmversemeopuauonofanon-minhnum-
plusesysmmshouldbeinvestigated. Naproblemhasbeerrreeearchedintheareaof

speech analysis.

mmmequanesofunnghneupmdicnmmdewnvolveaprocessmresmnfiomexdt-
inganalbpole filterwithaconelamdprccessshouldbeinvestigamd. ‘l‘hisprcblemlus

beenreeearchintheareaofpitchpulsedetectioninspeechpmcesses.

1fthedevelopmemofarnethodofidentifyingheartbeatsinthemicmwaveheartbeatsignal
bydewcfingdnngesmdunafiniesofthemiaowavesignflismbepunued.mwmdsof

detecfingchangesinmestadsdcsofstochasdcpmcessshouldbesmdied

36

ltispossiblethattheall-pole mteroftheBymemdSiegel (l985)nrodelismodelingtln
monitor. hmaybeuseftntoseehowchmgingmeconfigumionofmemcnitoremctsme
ccnligurationoftheall-pole lllter.’1heccnfigurarimofthemonlmrmaybeaffectinghow

wefllhnupredlcfioncanperformmnndaecnonoflnutbemindnmmavengmla

APPENDICES

SAMPLES OI" FILES FROM THE DATA BASE

37

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200
1004
(a) o- . t . j. ‘ 1 1" L '
f I I r j
0 2 4 6 8
100-
(b) 0" g . . . ' I ‘ l, I
-1m-4
I I . t 1 I
0 2 4 6 8
Time(aeccntb)
thtI'eAl. Cheetwallfllewithhumanaubjeetatrestmdholdinglleuh. (a)microwavesignal. (b)hand
poutialreferencesignal
200-1
100- 1 a
u 1 ‘1 . . ‘v 1 M . I ; 1
Q) 0- it 1 ‘ q .f‘ ,i . :_ . .' l ; ‘il
-lm-d I
4014
r 1 T r T
8 10 12 14 16
100-
0- l‘ I '
(b) ‘ ' ' ‘
“m T I I I 1
8 10 12 l4 l6
Tmre(seconds)
FrgIIeAZ. Cheatwalllilewithhumannrbjectatrestandhreuhing. (a)rnierowavesigml. ('b)hand

potentialsignal.

39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200.4
(a) o-I 4 ‘
-200-
I j I T #
8 10 12 14 16
lm-I
(b) °" '1 ‘
-100fi
I I I I I
8 10 12 14 16
Time (seconds)
F'rgureAB. Chestwallfilewithhmnsubjecteaereisedlrdholdmgbreuh. (a)microwavesignal. (1))
hard potential referurce signal
300
200-
100-
(8) o-
-100-
-200«
j I r I I
0 2 4 6 8
100-1
”-
(b) 0" i ‘
-50-
-100—
I I I I I
0 2 4 6 8
Time (seconds)

Figure A4. Chest wall tile with human subject exercised and breathing. (a) microwave signal. (to) hand
potential signal.

 

 

 

 

 

 

 

 

 

100—
(I) o- W '
4“)-
I I 1 I I
0 2 4 6 8
10)
”'I
o) °'* '1 1 ‘ :
.50-
am-
I I I I T
0 2 4 6 8
Tin-amends)

FigureAS. legfileofahumansubject. (a)micrwavesignd. (b)handpomtialreferencesignal

41

 

 

 

 

 

 

 

 

 

 

 

 

1m
50.
(a) 0- , ‘
-50...
I I I I I
0 2 4 6 8
100-1
(b) 0-1 ’ 3.1 3;. ' I ‘ I I. ,l"
I I I F I
0 2 4 6 8
SO—I
. . I II I
(C) 0-1 . a I ‘ (11‘
' I' ' J '1
-50-
I I I I I
0 2 4 6 8

Time (seconds)

FigureA6. lnanimaseobjectfilea. (a)microwavesignalforwoolsurface. (b)microwavesignal
for metal surface. (c) microwave signal for open room.

APPENDIXB

PREDICTION ERROR VARIANCES USED TO DETERMINE
ALLoPOLE FILTER ORDER

43

 

TableBl. mmvmuummmmw

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Prediction Error Variance
File Type Order
1 I 2 I 3 [ 4 I s l 6

Human Subjects at rest and holding breath.

Subject 1 1557 342 274 142 137 125

Subject 2 1129 454 349 167 152 144

Subject 3 4855 1217 886 474 421 376

Subject 4 2183 551 416 201 189 180
Human Subjects at rest and breathing.

Subject 2 587 219 162 63 59 56

Subject 3 4195 1115 784 351 305 247

Subject 4 980 295 225 92 88 86
Human Subjects exercised and holding breath.

Subject 1 3564 1098 781 325 272 248

Subject 2 2531 859 549 302 274 235

Subject 3 5833 1285 936 476 409 336

Subject 4 1965 563 388 152 136 119
Human SubjeCts exercised and breathing.

Subject 1 2858 1006 687 359 319 252

Subject 2 1925 614 442 208 1% 166

Subject 3 3287 1029 718 342 308 253

Subject 4 2237 ' 725 501 203 170 135
Human Subjects' legs.

Subject 1 2026 558 407 174 153 130

Subject 2 2028 624 408 194 176 153

Subject 3 985 289 208 110 105 101

Subject 4 1180 393 280 119 106 93
Inanimate Objects.
Wool Surface 659 316 276 201 198 188
Metal Surface 1415 566 484 292 275 228

Open Room 775 333 289 184 181 161

 

 

 

 

 

 

 

APPENDIXC

ALL-POLE FILTER COEFFICIENTS

AA

45

 

TableCl. Afl-Polemcm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

All-Pole Elm Cocfficierls
File Type A. 1 A2 [ As I A.
Hurrran Subjects at rest and holdjrrgbreath.
Subject 1 -1.864 2.397 -1.534 .7052
Subject 2 -1.898 2.298 -1.607 .7369
Subject 3 -2.055 2.562 -1.696 .7027
Subject 4 -1.984 2.512 -1.670 .7320
Human Subjects at rest and breathing.
Subject 2 -1.631 2.140 4.467 .7745
Subject 3 -1.991 2.526 -1.716 .7363
Subject 4 -1.931 2.431 -1.651 .7550
Human Subjects exercised and holding breath.
Subject 1 -2.117 2.548 -l.739 .6786
Subject 2 -1.980 2.426 -1.647 .6597
Subject 3 -2.081 2.576 -1.684 .6735
Subject 4 -2.047 2.630 -1 .806 .7732
Human Subjects exercised urd breathing.
Subject 1 -1.775 2.360 -1.594 .7788
Subject 2 -2.116 2.589 -1.780 .7189
Subject 3 -2.11 1 2.604 o1.781 .7223
Subject 4 -1.899 2.438 -1.687 .7792
Human Subjects' legs.
Subject 1 -2.025 2.551 -1.730 .7449
Subject 2 -2.049 2.561 4.739 .7129
Subject 3 -2.143 2.575 -1.734 .6786
Subject 4 - 1.991 2.482 -1.730 .7555
Human Subject Means -1.984 2.485 -1.684 .7273
Inanimate Objects.
Wool Surface -1.301 1.497 -0.831 .5089
Metal Surface -1.480 1.861 -1.220 .6830
Open Room -1.286 1.683 -0.989 .6064
Inanimate Objects Means -1.356 1.680 -1.013 .5994

 

 

 

 

 

 

APPENDIX D

THE RESULTS OF THRESHOme THE LIKELIIIOOD VARIABLE SEQUENCE
AS A HEARTBEA‘I' DETECTION METHOD

47

 

TableDl. TheResultsofThl'edloldlngtheWVaflablcSeqm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

as a Method of Detecting Heartbeats
Actual Number Number i Number '5
File Heartbeat of of Hits of False Alarms
Coum Clusters Hits False Alarms
Human Su ' at rest and holdggbreath.
Subject 1 20 19 17 85 2 10
Subject 2 l7 17 19 1m 0 0
Subject 3 23 24 19 83 5 21
Subject 4 24 23 19 79 4 18
Means 85 12
Human Sub' at rest and breathing.
Subject 2 14 20 14 1m 6 30
Subject 3 23 20 18 78 2 10
Subject 4 25 21 17 68 4 19
Means 82 19
Human Sub'ects exercised and holding breath.
Subjecr l 37 28 25 68 3 10
Subject 2 14 23 13 92 10 43
Subject 3 27 23 22 81 l 4
Subject 4 24 23 21 87 2 9
Means 81 17
Human Sub' cts exercised and breathin .
Subject 1 30 22 15 50 7 31
Subject 2 26 21 19 73 2 9
Subject 3 31 25 22 70 3 12
Subject 4 32 23 21 66 2 9
Means . 64 15
Human Sub'ects' legs.
Subject 1 23 20 14 60 6 30
Subject 2 21 18 15 71 3 16
Subject 3 29 18 12 41 6 33
Subject 4 35 18 11 31 7 38
Means 50 30

 

 

 

 

 

 

 

 

APPENDIXE

THE UNNORMALIZED PRE-WINDOWED LEAST SQUARES LATTICE FILTER

PARAMETER UPDATE ALGORITHM

This appendix gives the parameter update algorithm used for the Unnonnalized Pre-
Wlndowed Least Squares Lanice Filter. The algorithm came from Friedlander (1982a. p. 844).
The algoritlun found inFriedlanderisforthemulti-channel case. Thismeansthatall ofthevari-
ables in the algorithm presented in Friedlander are either vectors or matrices. The scalar case was
usedinthisthesisresearch. ‘l'hismeansthatallofthevariablesinthelattice filterupdate algo-

rithm were scalars. The scalar version of the algorithm is given in this appendix.

Input parameters:
M a maximum order of lattice
y-r - data sequence at time ’1‘

l an exponential weighting factor

Variables:

R's; :- sample covariance of forward errors

49
R534 a: sample covariance of backward errors
AP; 3 sample partial correlation coefficient
7;; a 1 - 79.1- : 1 - likelihood variable
apn- . forward prediction enors
rpg.‘ - backward prediction errors
Kg; - forward reflection coefficients

Kg; a backward reflection coefficients

The following computations will be performed once for every time step (Tao. . . .

Initialize:
Eo.r ‘ 1'o.'1' ' Yr
R63 " R6: ' 3363-1 + YrYr
751:1' 3 1
Do forp - 0 to minIMJ‘) .1

Ayn: ' MIMI-1 4' 5p.Trp.T-1N§-l.T-l "
731' 3 Vii-13' ' rp.Trp.T/R6.T "
KIM: " AMI/Rim "
Spot: = 59.1 - KpolJ'er-l
er-HJ' 3 R8,? ' K$+1.TA;»1.T
Kéorr = 159.131jo ‘

fpotfr = rp.T-1 ' K§+LT€pJ

. TMAX).

50

R843 ' 353-1 - ApHIKjgthT

Nore: Only thevariablesA.R‘.R'.f.rrreedtobestoredfrom onetimesteptotheother. They
are all set initially to zero. The quantities R'. 1‘. rrreed to be stored twice to avoid ”overwriting".

When the divisorx - 1‘. R'. R‘ is very small. set llx :- 0 in the equations marked with ‘.

~—_- I III III m

COMPUTING THE ALL-POLE FILTER COEFFICIENTS
FROM THE UNNORMALIZED LATTICE PARAMETERS

nusappendixgivesurealgonuunmawuusedtocompucdnan-polemmrcoemam
ficmmeUmrormalizedPre-W'mdowedleastSquuesutticefilmrm Thealgoritlln
camefromFriedlander(l982a.p. 845). ‘l'hetrarrsferftmctimroftheall-polsfilterhasbeen

rewfinenmmnsoumdremufionconespondsmunalgonumptuuledmddsappendix

Hall-pole [ma(1)- —-‘—-— . [El]
1 + 1:1“ is”

wherep is the order ofthe all-pole filter. The following algoritlln was and to update tin estima-
tion of the all-pole filter coefficients from the lattice parameters for each time step. Recall that
for the lattice filter of order M all lower order lattice filters are available in its structure. This
means that the parameters oflattice filters oforders lowerthanMare svailable huntheparame-
ter update algorithm of a lattice filter of order M. The following algorlttmr computes the
coefficients of the all-pole filter corresponding with the lattice filter of order M ltd the
coefficients of the allopole filters of all lower orders. The all-pole coefficiems are designated by

A“ where p is the order of the allopole filter.

51

52

NonthafirealgontlmmFfiedlander(l982ap.845)isfornnmulfi-chmmelcase. This
meansdrattheparametersofthealgoriuunareeithervectorsormatrices 'l‘hescalarcasewas
usedirrthisresesrelr. Thereforethefollowingalgoritlunisforthesealarcsse. 'l'hismsuthat

theparametersoftlrefollowingalgorithmarescalars.

Inputs:

M-maximumorderofthelatticc

r,- backwarderrorforthecurrenttlmestep
ygslikelihoodvariableforcurrenttimestep
Kgcfonvardrefiectioncoefficlentforthecurrenttimestep
Kgsbackwardrefiectioncoefficientforthetarrrenttimescp
R's-samplecovarianceforbackwardenorsforthearrrerrttimestep
Variables:

A,” all-pole filtercocfficients

Banach

Thaccomptnadomwfllbeperfumedesdrfimehisdesimdmupdaetheafl-polefilter
coefficients.

Initialize:
3,1480 for p80.....M-1
Con-0

Fori-O.....M

53
Aoj-Boj-l fori-O
Aoj-Boj-O forl>0
Doforp-O.....M-1
BFJ'Bu’prpJfi-t
amen-rm
MIJ'M‘WIBSH
3pm" Bar-1 ‘KéotApr-P‘ ll

APPENDIX G

A FORTRAN IMPLEMENTATION OF THE UNNORMALIZED
PRE-WINDOWED LEAST SQUARES LATTICE FILTER

TheUnnormalizede-WhrdowedlesaSquueslecefilterwasimplemmdmtwo
madmasuuctumholdhtgthelatficepamaasmrdflmpuamaerupdueflgonm. Micro-
softFortranwasusedfortheimplementaticn. Thehtficedamrmrcmreiscontainedinalabebd
commonblock. mlatficepmmnewrupdatealgoritlunisccmainedinasubmutine. Tlreparam-
eterupdatealgorithmistobecalledforeaehnewtimescp. TheFortrancodeforthelatticedata

structureandparameterupdatealgoritlunis giverrbelow.

AAAA‘JAA‘AJJAAAAAALAAAAAAAA‘AAAAAAAA AAAAJA ALLA—AAAAA‘AA‘AAAAAAA‘AAA‘A

vvv Viv vvv v v- v- va va

LATTICEDST

THIS FILE DEFINES TI-IE UNNORMALIZED PRE-WINDOWED LEAST SQUARES LAT-
TICE A1..GORITHM DATA STRUCTURE THE ALGORITHM WAS TAKEN FROM:

FRIEDLANDER. a. LATTICE mans FOR mm PROCESSING. PROCEEDINGS
OF rue rear-2. v01. 70. No.8. AUGUST 1982. pp. 342-344.

DEFINITIONS:

COMMON/LATTICE! . LABELED COMMON THAT CONTAINS THE LATTICE DATA
STRUCTURE

RE . ARRAY CONTAINING SAMPLE COVARIANCES OF FORWARD ERRORS. EACH
ELEMENT OF THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE

54

55

FORWARD ERROR FOR A PARTICULAR ORDER. NOTE THAT THEE IS AN
OFFSETBETWEENTHEARRAYINDEXANDORDEL ARRAYINDEXI
CORRESPONDSTOORDERO.

RR . ARRAY CONTAINING SAMPLE COVARIANCES OF DACKWARD ERRORS. EACH
ELEMENTOFTHEARRAY CORRESPONDSTOTHE COVARIANCE OFTHEmR-
WARD ERROR FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN OFFSET
BETWEENTHEARRAYINDEXANDORDER. ARRAYINDEX1CORRESPONIB
TO ORDER 0.

RRCOP‘Y - ARRAY CONTAINING SAMPLE COVARIANGS OF BACKWARD MRS
FORTHEPREVIOUSTIMES’IEP. EAO'IELEMENTOFTHEARRAY
CORRESPONDS TO THE COVARLANCE OF THE FORWARD ERROR FOR A PAR~
TICULAR ORDER. NOTE THATTHERE IS ANOFFSETBETWEENTHE ARRAY
INDEX AND ORDER. ARRAY INDEX 1 CORRESPONDS TO ORDER 0.

PARCORR -ARRAY CONTAINING SAMPLE PARTIAL CORREATION COEFFICIENTS.
EACH ELEMENT OF THE ARRAY CORRESPONDS TO THE COVARIANCE OF'IHE
FORWARD ERROR FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN
OFFSETBETWEEN'IHEARRAYINDEXANDORDER. ARRAYINDEXI
CORRESPONDS TO ORDER 0.

LHOOD - ARRAY CONTAINING THE LIKEJHOOD VARIABLE. EACH HEMENT OF
THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE FORWARD ERROR
FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN OFFSET BETWEEN THE
ARRAY INDEX AND ORDER. ARRAY INDEX 1 CORRESPONDSTO ORDER o1.

LHOODCOPY - ARRAY CONTAINING THE LIKELIHOOD VARIABLE FOR THE PREVI-
OUSTIMESTEP. EACHEIEMENTOFTHEARRAY CORRESPONDSTOTHE
COVARIANCE OF THE FORWARD ERROR FOR A PARTICULAR ORDER. NOTE
THATTHEREISANOFFSET BEIWEENTHEARRAYINDEXANDORDER.
ARRAY INDEX 1 CORRESPONDS TO ORDER -1.

EERR . ARRAY CONTAINING FORWARD PREDICTION ERRORS. EACH ELEMENT OF
THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE FORWARD ERROR
FOR A PARTICULAR ORDER. NOTE THATTHERE IS AN OFFSET BETWEEN THE
ARRAY INDEX AND ORDER. ARRAY INDEX 1 CORRESPONDS TO ORDER 0.

RERR - ARRAY CONTAINING BACKWARD PREDICTION RRORS. EACH ELEMENT
OF THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE FORWARD
ERROR FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN OFFSET
BETWEENTHEARRAYINDEXANDORDER. ARRAYNDEXlCORRESPONDS
TO ORDER 0.

RERRCOPY - ARRAY CONTAINING BACKWARD PREDICTION ERRORS FOR THE
PREVIOUS TIME STEP. EACH ELEMENT OF THE ARRAY CORRESPONDS TO
THE COVARIANCE OF THE FORWARD ERROR FOR A PARTICULAR ORDEL
NOTETHATTHERE IS ANOFFSETBETWEENTHEARRAYINDEXANDORDER.
ARRAY INDEX 1 CORRESPONDS “IO ORDER 0.

RE - ARRAY CONTAINING FORWARD REFLECTION COEFFICIENTS. EACH ELE-
MENT OF THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE FOR-
WARD ERROR FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN OFFSET
BETWEENTHEARRAY INDEXANDORDER. ARRAYINDEX 1 CDRRESPONDS
TO ORDER 0.

KR - ARRAY CONTAINING BACKWARD REFLECTION COEFFICIENTS. EACH ELE-
MENT OF THE ARRAY CORRESPONDS TO THE COVARIANCE OF THE

56

FORWARD ERROR FOR A PARTICULAR ORDER. NOTE THAT THERE IS AN
OFFSETBETWEENTHEARRAYINDEXANDORDHL ARRAYINDEXI
CORRESPONDS TO ORDER 0.

MAXORDER - MAXIMUM ORDER OF TIE LATTICE FILTER.

(NOTE: INDEX 1 CORRESPONDS TO TIE ZEROTH ORDER. EXCEPT FOR TIE LIKELI-
HOOD VARIABLE WIERE INDEX 1 CORRESPONDS TO ORDER -1. THIS INCON-
VENENT INDEXING METHOD IS DUE TO LIMITATION OF TIE FORTRAN COMPILER
BEING USED.)

AAAAAAAAAAAAAAA- ALA; .AAAAAAAAAAAAAAAA‘AAAAA;‘AAAEAA‘AAA‘AAAAAA‘A‘A

vvvaV—f v vv v1 v - vvv vv—

REAL RE(10). RR(10). RRCOPYOO). PARCORROO)
REAL LIIOODOO). EERROO). RERRGO). RERRCOPYOO)
REAL KEUO). KR(10). LHOODCOPY (10)

INTEGER MAXORDER

COMMON/LATTICE] RE. RR. RRCOPY. PARCORR. LIIOOD. LHOODCOPY.
EERR.RERR.RERRCOPY.KE. KR.MAXORDER

A..4-A..-‘-

SUBROUTINE UPDATELAT‘TICB( DATA. ORDER. WEIGHT. TIME. LIMLHOOD.
PARMLIM)

AAAAAAA‘AAA‘A‘AA‘AJA EAAAAAAAA AAA‘AAAA‘AAAAA‘J AAAAAAAA AAA

SUBROUTINE UPDATELATTICE

THIS SUBROUTINE UPDATES THE UNNORMALIZED LEAST SQUARES LATTICE
DATA STRUCTURE FOR A TIME STEP. THE UPDATE ALGORTTIN WAS TAKEN
FROM:

IREDLANDER. 3.. LATTICE FILTERS FOR ADAPTIVE PROCESSING. PROCEEDINGS
OF TIE EEE. VOL. 70. NO.8 AUGUST 1982. pp 842.844.

INPUT:

COWONMTTICEJ - LATTICE DATA STRUCTURE (SEE LATTICEDS'I')
ORDER - MAXIMUM ORDER OFTHE LATTICE FILTER.

WEIGHT - EXPONENTIAL WEIGHTING FACTOR FOR PAST DATA.

57

LIMLHOOD . IF THE ABSOLU'IB VALUE OF LHOOD OR LHOODCOPY IS LESS THAN
LIMLHOOD. LHOOD OR LHOODCOPY WILL BE CONSIDERED TO BE ZERO.

PARMLIM - IF ANYVARIABLES OFTHELATI'KE ELTER EXCEPT FOR LHOOD AND
LHOODCOPY HAS ABSOLUTE VALUE LESS THAN PARMLIM. THE VARIABLES
WILL BE CONSIDERED TO BE ZERO.

DATA . A DATA POINT FROM A DATA SEQUENCE.
TIME - CURRENT TIME STEP

OUTPUT:
COWONMTTICE/ - LATTICE DATA STRUCTURE

A‘A‘..A;AAAAAAA4AAA.¢AAAAA‘AAAAAAAAAAAAAA ‘A‘AAAA‘A;-AA “--‘--A“A_-AA

SINCLUDE: ’LATTICEDST'

REAL DATAWEIGHTJJMU-IOODPARMUM
INTEGER TIMEORDERJ’

" INTI'IALIZATION

HERRU) :- DATA

RERRO) 8 DATA

1250) I WEIGHT’REU) + DATA‘DATA
RRU) 8 R50)

LHOOD(1)- 1

“' LATTICE STAGE UPDATES
DO 100 P I l.(MIN(ORDER.11ME))

IF (LHOODCOPY(P) .LT. LIMLHOOD) THEN
PARCORR(P+1) a WEIGHT‘PARCORRG’H)
ELSE

PARCORR(P+1) . WEIGHFPARCORR(P+1)+ mm . RERRCOPYG’H
wooncowcp)

ENDIF

IF (RR(P) .LT. PARMLIM) THEN
LHOOD(P+1) 8 LHOODCP)
ELSE
LHOOD(P+1) a LHOOD(P) - RERR(P)‘R.ERR(P)/RR(P)

100

200

58
ENDIP

IF (RRCOPY (P) .LT. PARMLIM) THEN
KR('P+1) I PARCORR(P+1)‘ 0.0
EISE 7
KRCP+ l) I PARCORR(P+1)IRR(I)PY(P)
ENDIF

EERRCP-I-l) I EERR(P) - KR(P+1)‘RERRCOPY(P)
RE(P+1)I RE(P) - KR(P+1)‘PARCORR(P+1)

IF (RE(P) .LT. PARMLIM) THEN
KE(P+1) I PARCORR(P+1)‘ 0.0
ELSE
KECP-o-l) I PARCORR(P+l)/RE(P)
ENDIF

RERR(P+1) I RERRCOPYG’) - KE(P+1)‘EERR(P)
RRCP-H) :- RRCOPYO’) - PARCORR(P+I)‘KE(P+1)

CONTINUE

DO 2C!) P I IMAXORDER
RRCOPY(P) I RRG’)
RERRCOPYCP) I RERRG’)
LHOODCDPY (P) I LHOOD(P)

CONTINUE

RETURN
END

A FORTRAN IMPLEMENTATION OF THE ALL-POLE FILTER
COEFFICIENT UPDATE ALGORITHM

mul-polemtereoeffidanupdmdgofimmwhnplanmedinmmadum
mmmm-mmmmmammmmmm mafia»
mwasusedformeimplememadou. mmmmeominedinahheledmmuoch
‘mecoefficiemupdnealgofithmisconnimdham TheFormcodefwlhe

coefficient dam mature and the coefficient update 3130mm: is given below.

LATCOEFDST

THIS FILE DEFINES THE ALL-POLE FILTER COEFFICIENT DATA STRUCTURE. THE
ALGORITHM USED TO UPDATE THE ALL-POLE FILTER COEFFICIENTS WAS TAKEN
FROM:

FRIEDlANDER. 8.. LATI'ICE FILTERS FOR ADAPTIVE PROCESSING. PROCEEDINGS
OF THE IEEE. VOL. 70. NO. 8. AUGUST 1982. pp. 844-845.

NOTE THAT THE VARIABLES IN THIS DATA STRUCTURE SHOULD BE INITIALIZED
TO ZERO BEFORE THEY ARE USED.

DEFINITIONS:

59

60

A03.” - MATRIX CONTAINING TIE - ALL-POLE FILTER COEFFICIENTS. p
CORRESPONDSTOTIEORDEROFTIEFIIJTER. imRRESPONDSTOTIE
spscmccommmmpommmmmmm le
CORRESPONDS TO TIE ZERUTH ORDER.

303.5) - MATRIX CONTAINING PARAMETERS USED IN TIE ALL-POLE FILTER COEFo
FICIEN'T UPDATE ALGORITHM. p CORRESPONDS TO THE ORDER OF TIE
FILTER. i CORRESPONDS TO TIE SPECIFIC COEFFICIENT IN TIE p ORDER
ALL-POLE FILTER. p I l CORRESPONDS TO TIE ZERUTH ORDER.

BSTARQDJ) - MATRIX CONTAINING PARAMETERS USED IN TIE ALL-POLE FILTER
COEFFICIENT UPDATE ALGORITHM. p CORRESPONDS TO TIE ORDER OF TIE
FILTER. i CORRESPONDSTO‘TIESPECIFIC COEFFICIENTINTIEpORDER
ALL-POLE FILTER. p I1 CORRESPONDS TO TIE -1TH ORDER

C(pfi) - MATRIX CONTAINING PARAMETERS USED IN TIE ALL-POLE FILTER COEF-
FICIENT UPDATE ALGORITHM. p CORRESPONDS TO TIE ORDER OF TIE
FILTER. i CORRESPONDS TO TIE SPECIFIC COEFFICIENT IN TIE p ORDER
AUaPOLEFlTER. p- I CORRESPONDSTOTIEZEROTHORDER.

A‘AA‘A—LAAJA‘AA‘AA‘AAAAAA A4444A44AAAAA4AA‘A;AAAAAA‘AALAAJ -- AA A‘A‘JAA

REAL A(10.10). 300,10). BSTAROOJO). C(10.10)

COWONLA'TCOEF/ A. B. BSTAR. C

SUBROUTINE COEFCALCUIATION(ORDER.PARmm.LIMIJ-IOOD)

AAA—AAAAJAAAAAAAAAAAAAAAA‘AAAAAAAJ A AAAAAAA AJAAAA‘AAAAAAAAAAAAAAAALAA‘

TIIIS SUBROU'TINE UPDATES TIE ALL-POLE FILTER COEFHCIENTS WITH TIE
UNNORMALIZED PREoWINDOWED LEAST SQUARES LATTICE FILTER PARAME-
TERS. TIE COEFFICIENT UPDATE ALGORITHM WAS TAKEN FROM:

FRIEDLANDER. 3.. LATTKE FILTERS FOR ADAPTIVE PROCESSING. PROCEEDINGS
OF TIE EEE. VOL. 70. NO. 8. AUGUST 1982.. pp. 844-845.

INPUTS:
COMMON/LATTICE! - LATTICE DATA STRUCTURE (SEE LATTICEDST IN APPENDD(
C).

6]

COMMON/LATCOEF/ - ALL-POLE FILTER COEFFICIENT DATA STRUCTURE (SEE
LATCOEEDST).

ORDER-MAXIMUMORDEROFTIELATTICEFILTEL

PARMLIM . IFANY VARIABLES OFTHELATTICE FIIJTEREXCEPTFORU'IOODAND
LHOODCOPY HAS AN ABSOLUTE VALUE LESS THAT PARMLIM. TIE VARI-
ABLES WIIJ. BE CONSIDERED TO BE ERO.

LIMLHOOD - IF LHOOD OR LHOODCOPY FROM TIE LATTICE DATA STRUCTURE
HAS AN ABSOLUTE VALUE LESS THAN LIMLHOOD. LI'IOOD OR LHOODCOPY
WILL BE CONSIDERED TO BE ZERO.

OUTPUTS:
COMMON/LATCOEF/ - ALL-POLE FILTER COEFFICIENT DATA STRUCTURE (SEE
I..ATCOEF.DST).

AAAAA AAAAAAAAAAAALAAAAAAAAAAAAA AAAAAAAAAAA‘A

SINCLUDE: 'LATTICE.DS'T'
SINCLUDE: 'LATCOEFDST‘

REAL PARMLIMJJMLHOOD
INTEGER ORDERJP

DO 1000 I I I. ORDER+I

IFCI .EQ. I)TIEN
A(1.I)I 1.0
30.0- 1.0

ESE
A(1.I)-0.0
BUD-0.

ENDIF

DO 100 PI LORDER

IF (LIIOOD(P) .LT. LIMLHOOD) THEN
BSTAR(P,I+I) I B(P.I)
ELSE
BSTAR(P.I+I) I B(P.I) - RERRCP)‘C(PJ)/LHOOD(P)
ENDIF

62

E (ABS(RR(P)) .LT. PARMLIM) T'IEN
C(P+1.I) . C(PJ)
ELSE
C(P+l.l) - C(PJ) - WWBCPWCP)
ENDIF

A(P+I.I) I A(P.I) - KR(P+I)‘BSTAR(P.I)
WU) '- BSTARO’J) - KEG”) " A01)

100 CONTINUE

NIX) CONTINUE
RETURN
END

THE NORMALIZED PRE-WINDOWED LEAST SQUARES LATTICE mm

mmpauixgivesuupanmemupdmmuudfahmbedfie-
thoweduanSquuuLaniceFfltet.TbflgoritMcamemma9flLp.m.
Inthenormalizedversionofthelatticefilter.thelatticepametenmlimainmmvflueof
lwthanunity. firealgontlunfomidinFnedlanderisformmuld-CBIIIIMMW
thatallofthevariableeinthealgonrlunpruemedinFriedlanrlerareeitlumormmim
-mmdvcasewuusedmmhmmmmemmmofmmmmem
filterupdatealgorithmwerescalammscalarversionofthealgoritllnsgimmflsappendix.
PleasenoueumwhenFnedlanderusenTinampmenptcnpm-naeuinmemafindlat-

tice filterparameter update algorithm theT means transpose“ nattime.

Input parameters:

M I maximum order of lattice
y;- I data sequence at time T

I. I exponential weighting factor

Variables:

63

ST-eetimatedeovu-lmeeofyr
QT-mrmalizedforwardpredietionerrm
l‘fl.;-normalizedbaekwardpredictimerrm

K” - reflection coefficient:

KfiSaresetmzero
mmwingeompumwinbepedmmedoneeforeverydmeaepCP-O.....mm.

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intheequationsmarkedby‘.

65

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APPENDIX J

A FORTRAN IMPLEMENTATION OF THE NORMALIZED

PREoWINDOWED LEAST SQUARES LATTICE FILTER

mNomaflndPn-Wmdowedlquummeefiltamimplmdmtwopms.
adatasuucuneholdingthelatfieepammetersmdthepmameterupdatealgoflm Microsoft
Fom'anwasuedfonheimplunemation. NWMWBminedinahbeledoom-
monbloelt. mhtfieepameterupdatealgoriumiseominedirtambroutine. ‘l‘heparameter
updatealgorithmistobecalledforeaehnewtimemp. TheFortrmeodeforthelattieedata

mandpanmeterupdatealgorithmisgivenbelow. ('I'hisisaFortanversionofaprogram
thatwasdevelopedbyBetsyMatee-Needham.)

NLA‘I'TIQDS’T

THIS FILE DEFINES THE NORMALIZED PRE-WINDOWED LEAST SQUARES LATTICE
AWORTTHM DATA STRUCTURE. THE ALGORITHM WAS TAKEN FROM:

FRIEDLANDER. 3.. LATTICE FILTERS FOR ADAPTIVE PROCESSING. PROCEEDINGS
OFTHE [555. VOL. 70. No.8. AUGUST 1982, pp. 845-846.

66

67

DEFINITIONS:

COMMON/NLATI'ICE/ - LABELED COMMON TIIAT CONTAINS TIE LATTICE DATA
STRUCTURE

NEERR . ARRAY CONTAINING NORMALIZED FORWARD PREDICTION ERRORS.
EACHELEMENTOFTIEARRAYLURRESPONDSTOTIECOVARIANCEOFTIE
FORWARD ERROR FOR A PARTICULAR ORDEL NOTE THAT TIERE IS AN
OFFSETBE’I'WEENTIEARRAYINDEXANDORDER. ARRAYINDEXI
CORRESPONDS TO ORDER 0.

NRERR - ARRAY CONTAINING NORMALIZED BACKWARD PREDICTION mans.
EACH ELEMENT 0F TIE ARRAY CORRESPONDS TO TIE COVARIANCE OFTIE
FORWARD ERROR FOR A PARTICULAR ORDER. NOTE THAT ‘I'IERE IS AN
OFFSETBEI'WEENTIEARRAYWDEXANDORDER. ARRAYINDEXI
CORRESPONDS TO ORDER 0.

NRERRCOPY - ARRAY CONTAINING NORMALIZED BAGWARD PREDICTION
ERRORS FOR TIE PREVIOUS TIME STEP. EACH ELEMENT OF TIE ARRAY
CORRESPONDS TO TIE COVARIANCE OF TIE FORWARD ERROR NR A PAR-
TICULAR ORDER. NOTE THATTIIEREIS ANOI'FSET BETWEENTIEARRAY
INDEX AND ORDER. ARRAY INDEX 1 CORRESPONDS TO ORDER 0.

K . ARRAY CONTAINING NORMALIZED REFLECTION COEFFICIENTS. EACH ELEo
MENT OF TIE ARRAY CORRESPONDS TO TIE COVARIANCE OF TIE FOR-
WARD ERROR FOR A PARTICULAR ORDEL NOTE THAT TIERE IS AN OFFSET
BETWEENTIEARRAY INDEXANDORDER. ARRAYINDEX I CORRESPONDS
TO ORDER 0.

S - ES'INATED COVARIANCE OF TIE DATA SEQUENCE.

(NOTE: INDEX 1 CORRESPONDS TO TIE ZEROTII ORDHL THIS INCONVENIENT
INDEXING METHOD IS DUE TO LIMITATION OF TIE FORTRAN COMPILER BEING
USED.)

REAL NEERR(10).NRERR(10). NRERRCOPYOO). K00). S

COMMON/NLATTICEJ NEERRNRERRNRERRCOPYJLS

JAAAAAAAJAAAAAA‘A‘JJAAAAAAA AAAAAAAA‘AAAAA‘AAAAAAAAAA‘AJAA‘A‘AAAAA AAAA

w—vavv—v vv vv rvvvv vvvw—vv-r vvvvvvv vvvvv vvf vvv

68

SUBROUTINE NUPDATELATTIE(DATA.ORDER.WEIGITT.TIME)

AJAJAJ—‘AAAAAA‘AAA‘AJ‘A‘JAAJ t; EAAAEJJA-AAEJAA‘AEAAAAAAA‘AAA‘A"AA.AA.

SUBROUTINE NUPDATELATHCE

THIS SUBROU'TINE UPDATES TIE NORMALIZED LEAST SQUARES LATHE DATA
STRUCTURE FOR A NEW DATA POINT IN A INPUT DATA SEQUENCE. TIE UPDATE
ALGORITHM WAS TAKEN FROM:

FREDIANDER. 3.. LATHE FILTERS FOR ADAPTIVE PROESSING. PROCEEDINGS
OF TIE IEEE. VOL. 70. No.8 AUGUST 1982. pp 845.846.

INPUT:

COMMON/LATHE! - UNNORMALIZED LATHE DATA STRUCTURE (SEE
LATTICEDST IN APPENDIX C)

COMMON/NLATHCE/ - NORMALIZED LATHE DATA STRUCTURE (SEE
NLAT'I'IEDST)

ORDER - MAXIMUM ORDER OFTIE LATHE FILTER.

WEIGHT - EXPONEN'TIAL WEIGHTING FACTOR FOR PAST DATA.
DATA - A DATA POINT FROM A DATA SEQUENCE.

TIME - CURRENT TIME STEP.

OUTPUT:

COMMON/LATTICE] - UNNORMALIZED LATHE DATA STRUCTURE (SEE
LATTICEDST FROM APPENDIX C)

COMMON/NIATI'ICEI - NORMALIZED LATHE DATA STRUCTURE (SEE
NLATHCEDST)

AAAEJEEAAJEAAAJAn-A-nAAEAAAJEAJA-JJA .A‘AAA‘AAAAA‘A‘AAAA‘AJJ‘AEAJA AAEAA

v—v— vfrv vvvvvvv—v vvv if v v vvvv v—vvv

SINCLUDE: ’LATHCEDS'T'
SINCLUDE: 'NLATHEDST’

REAL DATA.WEIGI'TT.SQRRE.PRODUCT.F.INVF
INTEGER TIME.ORDER.P

1(1)

‘ INH'IALIZATION

IF ((ABS(S) .LT. .ml).AND.(ABS(DATA).LT. 000001)) THEN
NEERR( l) I 0.0
NRERRO) I 0.0
ELSE
S I WEIGHT'S + DATA‘DATA
NEERRU) I DATA / SQRT(S)
NRERRU) I NEERR( 1)
ENDIF

EERRU) I DATA

PRODUCT I 1.0
LHOOD(1)I 1.0

DO 100 P I 1.MIN(ORDER.TIME)

K(P+I) I INVF(K(P+1). NRERRCOPY(P). NEERRCP»
NEERRCPH) I FNEERRMNRERRCOPYCHKG-rl»
NRERR(P+1) I F(NRERRCOPY(P'). NEERRG’). K(P+l))

‘ CALCULATING LIKELIHOOD VARIABLE AND UNNORMALIZED FOR-
WARD PREDICTION ERROR

’ NOTE THAT THE FOLLOWING CALCULATIONS ARE NOT PART OF THE
NORMALIZED LATTICE FILTER UPDATE ALGORITHM.

LHOOD(P+1) I LHOODCP)‘(I - NRERRM‘NRERRG»
IF ('U'IOOD(P+1) .LT. 0.0) THEN ‘
LHOOD(P+1) - 0.0
ENDIF
PRODUCT I PRODUCT‘SQRTO - K(P+1)‘K(P+l))
SQRRE I SQRT(S)‘PRODUCT
EERRCP+1) I SQRT(LHOODCOPY(P+1))‘SQRRE‘NEERR(P+I)

CONTINUE
DO 200 P I IMAXORDER

NRERRCOPYG’) I NRERRO’)

200

.- A4A‘ AA AAA‘AAAAAAAAAAAAAJAAAAAA.‘ L‘AAAAA-4AAAAA;A
v' Tf‘f'fvvvv

70

LIIOODCOPY (P) I LI-IOODG’)

CONTINUE
RETURN
END

REAL FUNCTION P(A.B.C)

[F (C .GT. 1.0) THEN
CI 1.0

ELSE II: (C .LT. -1.0) THEN
CI 4.0

ENDIP

IF (3 .GT. 1.0) THEN
B I 1.0

ELSE IF (B .LT. 4.0) THEN
B I -1.0

ENDIF

X1 I SQRT(1.0 - C‘C)
IF (XI .LT. .(XXXXJI) THE‘I
INVXI I 1.0
ELSE
INVXI I 1.0/X1
ENDIF

X2 I SQRT(1.0 - B‘B)
IF (X2 .LT. .ml) THEN
INVXZ I 1.0
ELSE
INVX2 I 1.0/X2
ENDIF

-A.--..-.._.,A

71

F I INVXI‘(A - C‘B)‘INVX2

RETURN
END

AAAA A AAA AAA AA AAAAA AAAAA AA AA A

REAL FUNCTION INVF(A.B.C)
REAL A.B.C

IF (C .GT. 1.0) THEN
CIID

ESE IF (C .LT. 4.0) THEN
C I 01.0

ENDIF

IF(B .GT. 1.0)THEN
BI 1.0

ELSE IF (3 .LT. 4.0) THEN
B I-1.0

ENDIF

RETURN
END

AAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAA

APPENDIX K

REVIEW OF THE DEVELOPMENT OF
THE MICROWAVE VITAL LIFE SIGNS MONITOR

museofamictowavedeviceinthemeasuremofhmnanheanmeunbefoundin
Byme, Hynn. Zapp. and Siegel (1986). Byme and Siegel (1985). Byme. Zapp. Flynn. and Siegel
(1985). Hoshal, Ivkovich. Siegel. and Zapp (1984). Hoshal and Siegel (1986). Hoshal. Siegel. and
Zapp (1984). Lin. Kiemich'. Kiemicld. and Wollschlneger (1979). and Popovic. 01811. and Lin
(1984). mmmmmmmmuumdonofmeworkmmdevdofinga
bean rate ectimation method for the Michigan State University Biomedical Signal Ptocecsing
Laboratory’s microwave vital life signs monitor (Byme et al.. 1986; Byme & Siegel. 1985; Byme
et aL. 1985; Hoshal. lvkovich. et 11.. 1984; Hoshal & Siegel. 1986; Hoshal. Siegel. et aL. 1984).
Thisappendixwillmiewdnhismryofmedevelopmemofheanratemeammnemwdufiques

for the Michigan State University unit.

The First Michigan State University Microwave Vital Life Sign: Monitor

The first version of the Michigan State University microwave vital life signs monitor was
used by Byme. Flynn. Zapp. and Siegel (1986). Byme and Siegel (1985). Byme. Zapp. Flynn.
and Siegel (1985). Hoshal. lvkovich. Siegel. and Zapp (1984). Hoshal and Siegel (1986) and

73

Hoshal. Siegel. and Zapp (1984). Figure K1 is a block diagram of the device. A description of
the device's operation was found in Hoshal. lvkovich. not. (1984) and l-loshal. Siegel. eral.
(1984). in the monitor. a portable hornodyne transceiversystem is responsible {unwitting a
low-level microwave signal “detecting Dopplershiftsintheremmedsigml. ‘l'hemicrowave
transceiver emits a 10.5 CH: continuous waveatalevel ofa fewmilliwatts (more recetavetsions
ofthe instrument use pulsed transmitters). The returns ofthe microwave signal simply an analog
signal of only a few microvolts to the Doppler shin detector. After Dopplershia detection. the
low-level analog signal is sent through an amplifier that provides GOdB to 80dB of signal
amplification. After signal amplification. the analog signal is filtered with a bandpass filter. The
bandofthe filterwasplacedat 1-30l-lz. ‘l'heaelectionoftheaol-lzcumfl‘wasbaaedonthespee-
tral analysis of signals resulting from reflections of microwave signals of! the chest walls of
human subjects. There were no significant spectral components ofthe microwave heartbeat sig-
nalspaStBOlleioshal.Siegel. & Zapp. 1984). ‘lhelowendcutoflofl l-lzisuaedtoeliminate
any DC component in the signal and minimize breathing effects (M. Siegel. perms! communica-
tion. 1988).

The amplified and filtered analog signal is sampled by an eight-bit analog to digital con-
vener. The sampling rate varied from 96 to 128 samples per second in the above studies. The
final destination of the digitized microwave signal is a microprocessor. The final heart rate esti-
mation algorithms will reside in the microprocessor unit.

In order to evaluate the success of any heart rate measurement method. a reference of the
actual heartbeat activity is traded. A heartbeat reference signal was successfully chained from
an in-house designed unit that measures body surface potential between the hands of a human
subject The output of the device closely resembles an EKG signaL Hand potential signals were

simultaneously recorded when microwave heartbeat measurements were taken.

74

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75

Review ofthe Development ofa Heart Rate Ertlntation Method
for the Michigan State University Microwave Vital Life Signs Monitor

Peakdetection.

Pakdetecdonwuthefirnmethodcaflduedindndevewwahemnteafimfion
technique. lnanuncluttered signaLthemicrowavemeastnementsofaheartbeatresembiesa
heartbeatoccurrenceinaan. Largepenksinthemicrowavesignalcorrelatewithtln
occunutcesofheanbeatsfitelargepeakscanbelocatedafithpeakdetecfim

Peakdetectioniseffectivefororflyaresuicmdsetofoperatingcondidona Thesubjeet
mushemwduflbmadfingmwhflydufingdnremrdingofdumkrommm
uansceivermustbeplacedamuyslnndimawayhommdtenwaflofdnmbjea. There
mustbelittle interferencefiombreaufingorbackgrotmdmovememinthebopplershimd
encoded heartbeat signal. Under realistic operating conditions. the heutbeat signal may be
obscured by background noise and clutter. Peakdetection tedtrtiques applied to themicrowave
heartbeat signal are unreliable for realistic operating conditions (Hoshal. Ivkovich. Siegel. a
Zapp, 1984; Hoshal. Siegel. 8t Zapp, 1984; Byme a Siegel. 1985).

Correlation Techniques.

The next stageofthedevelopment ofaheartrate estimationteclmiquewasbasedonutiliz.
ing the periodic nature of heartbeat occurrences in the microwave signal. Peak detection failed
because ofthe high level ofclutter in the microwave signal. Hoshal. lvkovieh. Siegel. and Zapp
(1984) and Hoshal. Siegel and Zapp (1984) posed the following argument: lfcorreiation tech-
niques are useful in detecting periodic signals that are completely obscured by random misc. tier:
correlation techniques may be useful in extracting the heartbeat signal from the microwave meas-

urements. Autocorrelation was performed on the Michigan State University monitor microwave

76

heartbeat signal by Hoshal, lvkovich. eta]. (1984) and Hoshal. Siegel. etal. (1984). Lin. Kier-
niciti. Kierrticki.ar1dWollschlaeger (1M)mhwfiqmwm(1984)alsouwdauto-
conelafionmaflmateieanmsefiomamiaowuehartbeatsignal. Boshahlvkovidaeral.
(l984)andHoshal.Siegel.eral.(l984)showedthatautocoflelationcouldbeuaedtoacctnately
meammhemmebtndusetofopemfingcondifimundmmmemmcondafimmm
was limited. Anumber of problemswereencounteredwhenheartmteestimation methods using
autocorrelation were more rigorously tested.
nuabifityofmmconeudonmahodsmsepameasignalfiomomnngmiseisdepah
deruondtesignalbeingpenodieflummheartbeatsuepaeudopenodicevenn. ‘l'hetimeperiod
betweenheartbeatsmaynotbeconstantmymeafiegel. 1985; Hoshal &Siegel. 1986). The
leesuteheanbeatsueperiodicmemorethemtocorreladonpeaksbroaden. Anaccm'ateestima-
fionofdreheatratecammbeobtainedfiommebroadatedanoconeiafionpeaks.
mlmgthofmepaiodsbaweenheanbemsanchmgeabmpdy.nImmcondafiondme
mmwimmmmmmmmmaarwmmmmmm
changesin heartrate (Byme a Siegel. 1985; Hoshal& Siegel. 1986). Whentheperiodsbetween
luaubeauuemgrdualonguamoeondafimfimewhdowisdedmflednceitwofldrewhm
moreaccurateestimatesofautocorrelationpealtlocatiom (BymedrSiegel. 1985). Atradeoff
munbemadeindnsingafimewhdowlwflifaumcomhfimkwbeusedinesimadngm
ratefromthemicrowavesignaL ‘l'hisisaclassicaltime-frequencyresolutionproblem.
ltwasalsofounddmumsigmmreofalnutbeatoccunenceinutemiaowavesignalcan
changenotodyfiompmsonmpersonbmfiomheanbeatmheanbeatmyme&Siegel. 1985).
Autoconelationtechniquesdependonrepeatedbehavior. lfthesamepattemisnotrepeatedin
themicrowavesignuforuchocamenceofaheanbeanmeefi‘ecfivmessofamoconehfionasa

heanbeatsignal detectorwill belilniied.

77

Theabnityofauwconehfionwexnamdtemdgmlhunmemiaowavemeanne-
mermisfinunrmidennmdedbydnpresuweofpenodicbaekpomdcompmnmynut
Siegel.1985).‘l'hemostdominantperiodiceomponeraishreathing. ltisdiffiatlttofilterout
bmuhhtgbecwsedwmhmpfiorhnwledgeofanmjem'smgrmdnnngdemiuowan
measurementofthesubjeet'sheartrate. Becausethebreathingratemayhecloaetotheheartrase
andmanytimeslargerinamplinrde.u1eproblanofremovh1gd1ehreathingcomponaliscmno
pounded.

Vanafiominmeheanbeasigmliuvefimheddnnmofushtgamconehfionmesfi-
mateheartratefromthemicrowave signal. HoshalandSiegel (l986)ohservedthatvariatiatsin
thelevel of the microwave signal clutteralsoeffectedtheperformance of mtocotrelation. Auto-
correlationwastmreliableincasesoflowsignal-to-noinratioam)orhighciutterlevel
environments (Hoshal a Siegel. 1986). Experimental measurements showed that obtaining a
sufficiently highSNRcannothedone consistently. ‘lheSNRwasstrongly aflectedbytheposi-
tioning of the microwave transceiver overthe body. The unpedictable rate and strength of the
breathing motion alsoaffected their abilitytoobtainaconsistentSNR.

l-loshalandSiegel (1986) posmlatethatsignalandcluttervariationswillbecorneaneven
bigger problem when the microwave monitoristoheusedinthefield. Theheartramestitnation
technique mustbe able to contend with uncontrollable background clutterandpathoiogicalheart
conditions. Hoshal and Siegel call for a robust signal processing methodology. A methodology
thatcanmakeareasonableestimateoftheheartratefromthemicrowavesignaldespitethepossi-

ble variations in the heartbeat signal and background noise that might be encountered.

The Hoshal and Siegel Stochastic Model of the Microwave Heartbeat Signal.

The approach Hoshal and Siegel (1986) took to develop a robust heart rate estimation

method was to formulate a stochastic model of the microwave heartbeat signal in order to gain

78

knowledge about the statistics of the microwave signal. The knowledge gained was then used to
aid in the development of an optimal processing technique.
Hoshal and Siegel model the microwave heartbeat signal as
y(t)-x(t) ‘ ho). (K1)

where ‘ denotes convolution. y(t) is the microwave heartbeat signal. 3(1) is a pseudo periodic
irnpulsetraindefined by

x(r) :- 6(r-To) + 8(r-To-T1) + + 50- $119+ . . . . (K2)

wherenisatimeseriesformedfromsucceafivebeat-to-beatperiods. 5(r)isthehasavalueof
onion-0. Otherwise.5(r)isaero. lt(r)representsthetimedomainresponsecharacteristicsof
asingleheartbeatcycle.
‘lheheat-to—beatperiodsequence.T.-.ismodeledasa4thorderautoregressiveprocesa. The
panmmemofuwnmoddwembasedonnmeinmwakhetweenheutheatocamencesinue
handpotentialrefercncesignals. Asixpole.sixzeropole-aeromodelisusedforlr(t). The
parameter estimation for Mr) wasbasedonmicrowavesignalstakenfrom 10 subjects. Back-
groundnoisewasmirfimaldunngurerecordingofdresigrtals'l‘hesubjectswerelyingontheir
backswhilethemeasurementsweretaken. HoshalandSiegelO986)donotstatewhetherthe
monitorwasplawddirecdyonthechestwalloratsomedistancefromthechestwallofthesuh-
jects.
ThemoddwasdnnusedmesfimatemepowerspecualdensityofthemimowavedgmL
Mcmwwengnflswemsimmamdforvanmmeansmdvuianoesofmemoddpammaera
Thepowerspecnaldensityoftlnsimulatedmiaowavesignalswereobtained Distinctharmonic
peakswereseeninthepowerspectrumofeachsimulatedmicrowaveheanheatsignaLevenfor

thesignalswiththeworstcasesoftheparametersvariances.

79

mumevaryingmmmofamman'sheutmeanddnhmmficpeaksinmepowermee-
ualdanityofmenmulaedmicmwavedmakmggesedmfiomuandSiegdmaadapfive
comb filteringmaybeanappropriateteciatiquemestimaeheartrate. Asdescribedinl-loshal
andSiegel (1986).u1eadapfivecombfilwrsemdresdncomponunsofdnhipmdgnflspeeuum
forabestfittoaspecifiedmnnberofhannonicanyreiatedsignalcomponm Nonhmonic
componentsareattenuated. mbestfitfirndameraalfrequencyisdnestimneoftheheanrac.

Resultsofpmfimmarytestsonduadapdvemmbfilmfsabflitymesfimatehemmem
givenini-loshalandSiegei. (1986). Theadaptive comb filterwasappliedtosimulmedmdactual
microwave data. The simulated data consisted ofaseries ofmicrowave heartbeats generudby
theHoshalandSiegelmodeladdedtoband-litnitedwhitemiae. Threaltnicrowavedatawas
mkutmrderdwsamecmrdifiomumemicmwavedauuedmudmatednllodmmdfiegd
modelparameters. madaptivecombfiltergaveacetnaseestimmsofthelzartraesforbmh
simulated and real data.

Although adaptive comb filtering shows promiseasamethodforeatimatinghearttatefrom
themicrowavesignaqur-therinvestigationismded. ‘l'lul-loshalandSiegelmodelisbasedon
datarecordedunderidealconditions. ‘l‘hemodelneedsmheexpandedmincludepathoiogical
heartbeat behavior and the affects of breathing and background clutter (Hoshal a Siegel. 1986).
Theabilityofthecombfiltertoadapttoabmptchangesinheartratencedstobeinvestigated. It
must be determine that the adaptive comb filter technique can give accurate heart rate esfimates
for microwave heartbeat signals cluttered by breathing and backgroundtnovements. The robust-

tress of the adaptive comb filter has yet to be provcrt

The Byme and Siegel Stochastic Model of the Microwave Ileartbut Signal.

The approach that Byme and Siegel (1985) took to find a robust heart rate estimator is simi-

lar to approach taken by Hoshal and Siegel (1986). Byme and Siegel postulated a model for the

8O

microwaveheartbeatsignalandthenusedthemodeltoappiyanadaptivefilterintheestimation
ofheartrate. 111eBymeandSiegelmodelissimilartotheHoshalandSiegelmodelbutdre
choice of adaptive filtering is different.

ByrneandSiegel (l985)modebdthemicrowaveheartheatsignalastheoutputofanall—
polefilterdiatisexcitedbyatrainofimpulsesaddedtowhitenoise. 'IheByrneandSiegel

model is shown in Equation K3.
y(t)-[x(t)+W(t)l " Mt). (K3)

where" denotes convolution. y(t)isthemicrowaveheartbeatsignal. x(r)isthepseudoperiodic
trainofimpulses.EquationK20fthel-loshaland$iegel(l986)modelcanbeusedtodefinex(r)
ofthe Byrne and Siegel model. 190) is a band-limited white process. an) is the impulse
respomeoftheall—polefilter.1'herespomeofthean-polefilterexcitedbyoneimpulseshould
resembleamicrowavesignalheattbeat. ThistnodeldiffcredfromthefioshalandSiegeimodelin
twoways. ‘l‘hel-loshalandSiegelmodelusedapole-zerofilterwherethefiyrneandSiegel
mowuseaanall-polefilter. Seoondly.theByrneandSiegelmodelincludeswhitenoiseasa
componentintheexcitationprowssofthemodel.

‘l'heprimary motivation behindusingthe Byrne and Siegel (1985) model forthemicrowave
Inanbemngmlwauusueceaofapplyingasimflumoddmmeprohlemofdemmgphch
pulsesinvoicedspeech. TheparficularpitchdetcctionteciuuquethatpromptedfiymeandSiegel
toadoptthemodelinEquatioan wasdevelopedbyleeandMorf(l980). Voicedsoundssuch
asvowelsoundscanbemodeledastheoutputofanall-polefilterexcitedbyapseudoperiodic
trainofimpulses. ‘I'heimpulsetrainmodelsthepitchpulses. Theall-polefilterofthespeech
modelrepresentsthevocaltract. lnspecdrmalysiaitisofimeresttodemrminetheperiod
bemeendnpimhwlsesLhnupndiefioncmbeusedmhvemefleaH-polefihu'smspome
and recover the pseudo impulse train that excited the all-pole filter. The recovered impulses

appear as large prediction errors at the output of the linear predictor. (Appendix 1. reviews the

8i

relationslupbetweenureBymeandSiegelmodelandlinearprediction.) Fordiffererasounds.the
vocaltractwilltakeondifferentconfigurations. lnordertoinversetheefi'ectsofthevocdtract
ondupimhpflsesbyfimuprediaimmcmfigmadmofdnvocflmmbedmined.
‘l'heproperconfigurationoftheall-polefiltermodelmightrmtheknowrrormigiadnngewidtin
aspecchprocessAdapfivelheupredlcfimkumdmdemrminednmtnowncmfigmafimof
thevoealtractmodel.

BymeandSiegel(1985)modeleddteoccunenceofheanheatsasapaeudoperiodiehnpulse
train. Thednstwan.micmwave.mimowavedmmelmdmafimrhtgmfituemoddedwim:r
all-pole filter. lftheByrneandSiegel modelisvalid forthemicrowaveheartheatsignalsJineu
pmdicfimunbeusedmmmverdnlemheuimpflsemmednspeechmusym
dreheanbeatimpulseuainexcitesmightnotbeknownormiglndrmgeinfime Assumingtheir
modelivaBymemdSiegdusedadapfiveflmarpredicdonmdaeminethecmfigmof
thesystemmodel. Onceureheanbeatimpulsesarerecoveredduoughadapdvehnearptedicdon.
BymeandSiegdhopedmeaimamdwhtstanmmouslnanmebymeamringthepedodbaweat
consecutiveimpulses.

lnLceandMorf(l980).therecoveryofpitchimpulseswasenhancedbytheuaeofa
parameteroftheparticularadaptivelinearpredictortheyused. T'heparameterisrelamdndte
log-likelihood function ofthespeechprocessinputto the adaptivelinearpredictor. T'heparameo
terisameasureoftheunexpectednessofdremostrecemdatapointsofthespeechptocessCFried-
lander. 1982a). Sudden large changesinthis variableweregood indicators of theoccunenceof a
pitch pulse. Byme and Siegel used this parameterinthesame waytoenhmcetherecoveryof
heartbeatoccurrences.

lftheByrneandSiegel (l985)method ofestimatingheartrateisvalidformicrowavemeat-
urcments. the primary advantage ofthemethod over autocorrelation isthatthedctectionofthe

heartbeats is not dependent on the periodicity of the heartbeat. With the Byrne and Siegel

82

meMdnoecunenceofahembeuwuldbemmgnizedbydnmofaspedflevauu
theoutputofanadaptivelinearpredictor: drepresenceofalargepredictionerrorandanabnrpt
largechangeintheliltelihoodparameter.
11:3ymemdSiegel(l985)leutbeudeccdontecimiqtnwuudhaveacompuufimul
advantage overautoconelation. Byme andSiegel (l985)experimented withamrmber of dif.
ferentadaptivelinearpredictorsandfomtdthehestresultstocomefromanonnalindleast-
squareslatticefinenamrmaliaedversionofureadapdvefineupredimorusedbyleemdMorf
(1980). The filter is a recursive algorithm. The parameters of the adaptive lattice filter are
updated foreverynewdatasampleinputtothefilter. Autocon'elationprowssingrequiresblocks
ofdmuraeforeureteisafimedelaybetweenestimatesoftheheanrate. ‘lhelatticefilterstruc-
uneanowsforupdamsofheanrateesfimadonwimeverynewinptndatasunple
ThepafmmanceofmenymmdSiengMheumeadmecfionmchueisimprep
sive. Microwave signals obtained from subjects lying fiat with the microwave monitor mourned
directlyonthetheirchestswereprocessed.ByrneandSiegelobtainedlargepredictionenorsand
lugedrmgesmmefikefihmdparmaerdmguumnencesofheanbeamnuexmdming
ofheartbeatoccunenceswasdeterminedbyhandmtitreferencesignals. Aftertheerrorswere
mukedbydrdefivadveofdulikefihoodpammmermeakdaecfionwuusedmdmhndu
locationoftheheartbeats. ‘l'lreheartbeatsignalwassuccessfirllyrecoveredfromdrese
micmwavedgnals.NowdmtamoconelafionmuMhavebeenusedwesfimamdeheannte
becauseoftheregularityofthedataandthelackofclutter.
lnortlertomorerigorouslytesttheBymeandSiegelheartbeatdetectionmethod.adaptive
linearpredictionwasappliedtomicrowaveheanbeatsignalstakenfrom subjects placedthreefeet
from the microwave monitor. The subjects were seated and had exercised. Having the subjects
sitting is considered to be a more hostile condition for heartbeat detection compared to lying

down. in the sitting position. it is felt that the heart impinges the chest wall to a lesser degree

83

thantheifthesubjectislying downMSiegeLperaonalcommurficatiat. l988).‘l'heheartbeat
signalwasobscuredinthesemeasurements. Unlikethesignalsrecortiedforsubjectalyingdown.
autocorrelationfailedtogiveaccurateheartrateestimates. T'heuseofthenormalizedadaptive
lancemtumedicdonenmandhkefihoodpanmwmconnsmlymesimamsofdn

instaraaneousheartrateofthesubjects.

CurrentlnterestinthebevelopmentofafieartkateEstlmation Technique

Thecunuuintereainuredevelopmemofateeiufiquemesdmateheutmefordte
microwave vital life signs monitor is to formulate a real-time implementations of the most
promisingheartrateestimationtecimiques. Thereal-fimeimplernentationswouldbeusedon
boardtheheartratemonitor. 'l'heheartrateestimationteclmiqueadevelopedbylloshalurd
Siegel (1986) and Byrne and Siegel (1985) were implemented and mated independent of the mon-
itor. Recordeddata fileswereused. Theinitialpurposeofthisthesisreaearehwastodeveiopa
real-time implementation of Byme and Siegel adaptive least squares lattice filter estimation
method.

Although Byrne and Siegel (1985) showed an: the adaptive lattice filter tedmique worked
well under adverse conditions. the technique had not been fttlly tested. The teclmique was tested
withorrlyafewdata filesandtheresultsshowninByrneandSiegel(1985)wereofcasesin
which the technique worked very well (M. Siegel. personal communication. 1988). Before a
great deal of effort was expended irt developing a real-time implementation of the Byrm and
Siegel technique. more extensive off-line testing of the algorithm was performed.

A number of problems were encountered in the attempt to repeat the results of Byrne and
Siegel (1985). The source of these problems was trawd to differences iii the character of current
microwave heartbeat signals and the data used in Byrne and Siegel (1985). The differences might

be the result of two actions. First. a number of modifications have been made to the microwave

84

unit sirroe the Byme and Siegel study. Second. the standard testing position of the microwave

monitor and subject has changed.

The Modified Michigan State University Microwave Vital Life Sign Monitor.

FigumKZshowsablockdiagmnoffirearnufimiaowavevitalfifesigmmmfitor. Four
majormodificationsweremade. Allthechangesweremadetotheanalogsignalprocessingaec-
tionofthemonitor. mummifiedmicrowavesignalwaschangedfromacontinuouswavetoa
pulsedmierowave. Thismodificationwasmadetoimprovethesafetyofsubjectsdurhtgexpo-
motdnmiaowavehannnisfionmdmmmimizepowuconmmpSMMSiegel.pumnfl
communication. 1988). Alogarithmic amplificrwasaddedtoincreasethedymmicrangeand
sensitivity ofthe microwave transceiver. Thelogarithmie amplifierincreasesthesystems sensi-
fivitytonnansignalswhflelargesigmhamnotallowedmsamratedresysm. Anautomatic
gaincumolmfitwuaddedwmamemptummedamwocesnngsecdonofmemommrwmud
haveanevenlevel. Theband-passfilterwaschangedtoaswitchedcapacitorfilter. This
modification allows the microprocessor unit of the monitorto control the characterof the band of
the switched capacitor filter during operation of the monitor.

Theanoflfiequendesofmesudmlmdcapuhormterrunainedmtmdunngdfismesis
reaeuchThelowfiequuicyctu-oflwu4ilzanddtehighfiequencymn-offwulsflz The4
Hzart-offwaschosenmfiltermnsignflcomponurtsrelatedmbreathingandsuflallowharmon-
icsoftheheartbeatsignaltopass. ltisbelievedthatmosthreathingcomponentsarefomrdator
below4 l-lz(M. Siegel. personal communication. 1988). The 15 Hzcut-off wasused to reduce
noise. mamaspecnummalysisofthemicmwaveheanbeungmlsmwthadumwerem

significant heartbeat signal components above 15 H: (M. Siegel. personal communication. 1988).

The current standard positioning of the monitor and the subject are different titan the posi-

tioning used in Byrne and Siegel (1985). errent mic1owave data are recorded with the subject

.38... she o... a... 2.3.5.... 9.5.2: as... 5.20.2 3.3... an. .9. 2......

 

.2180 —

 

 

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5.3.2... o: n.-.
3...". 5.896
3.2.3

 

 

 

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3.... 1.. 2%....

 

 

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86
sitting. ‘l'hemonitorisplacedsixinchesfromthesubjectsehestwall. Themonitorisplaced

slightlytotl'releftofthecenterofthechestwall. Thesubjectsaresittingratherthanlyingdown.

APPENDIXL

REVIEW OF THE RELATIONSHIP BETWEEN
AUTOREGRESSIVE PROCESS SYNTHESIS
AND ADAPTIVE LINEAR PREDICTION

An autoregreesive (AR) process is modeled as
ytnr-gmtn-nwtnr. (1.11

wherey(n)isdreARpmcesthcag’suemeARmoddpameternmeaawifiteM
andM istheorderofthemodel. AsampleofanARfime-aeriescarbeertpresaedasalineu
combination ofpastsamplesplusasample fromawhiteprocess. Themrmberofpastsampies‘m
thelinearcombinationistheorderoftheARprocess. Thetimeinmrvalbetweensampieshcon-
stant.
EquationllshowsthattheARprocesscanbemodeledastheoutputofanall-polefilter

excited by a band-limited white process.

rm- ‘ 4 We). (12)

9“!

88
Themodelin(l.2)wasfonnedbytaltingthea-transformofa.1)andueatingW(z)astheinputto
asystemandY(z)astheoutputofthesamesystem. AftmdamentalgoalofARmodelanalysisis
todeterminetheparametersoftheall-pole filter. Linearpedictioniscanusedtoestimatedre
coefficierusoftheARmodel all-pole filter.

UnearpredicnonesumnesurenmndamsampleofmARprocesbyafineucombmaficn

of past data samples.
rtn) - gluon-t). (ts)

w11erey(rt)estimaaesy(n)andb. isalinearpredictioncoeffieieru. Theraedictionerroris
definedinCIA).

¢(fl)')'(fl)'gba3(fl‘k)o (IA)

wheree(n)isthepredictiorrerror. Bytakingthez-transformoftheerrorequationandtreating
dnpmdicdonmmrumeouqanofasysmmmdtheARpoceuuumhmtnofdnsamesysmm.
MshomdmfinarpmdicfionmnbeviewedudninvemeoperafimofARprmsymheds
(l-layltin.l984).

£(z)- [1 -‘gb.z'*] m) (1.5)

89

linearpredlctiondeconvolvestheARraocesa. lfthepredictionenoraequemeisviewedasthe
mormmmwmmmmmmmummnm
ingtheARproaeasthroughman-zerofilter. lfthepredictiorrcoefficierasarethes-neastheAR
modelpuameeramuepmdicuonenorisdnsuneuunwlfimmhwdmen
modelall-polefilter. ThelinearpredictioncoefficierascanbeucdmesdmatetheARmodel
parameters.

l-lowarethelinearpredictioncoefficientsfound? lfthepastvahresofanARproceasand
dnmlafiomhipbetweendmsepastvaheaammmemlydungdnmcammwediam
drenextvalueoftheprocessisthesamplefiomthewhiteprm Tlnpredictionerrnrwillcmr—
tainthewhiteproaesssample. lfthelinearpredictorcmheuaedtoertnacttheputoftheprooess
umpiematisconehwdwimdtepaapmceusmplesmupredicnonmwmbemal

lfdiestafisucsofmeARpmcessbcingmalyaedueknownawaymopfimiaemedre
sdecfionoffineupmdicfioncoeffidamisbymminfidngfinma-dfinammedpediaim
amr.£{e1(n)}.1heparmemrsofunpredlcmrueumqudydewrufimdbymemwnd-mdu
statisticsoftheprocess. TheYule-Walkerequafionsgivealinearrelatiatshipbetweentheped-
ictor parameters and the autocorrelation coefficients. {Raj-OJ) where R; IE{y(tt)y(a-i)}.
mopfimumemsqumedemrpmdicmrmdeleaaaquarupredicmrcaheobtdmdbyauw
ingtheYule-Walkerequations.

lnmostapplications.thestatistiesoftheprocessarenothrownandmustheeatimatedfiom
data. OMtheprocessstatisticsaretime—varying. lnordertotrackthechanglngsutisticsofa
non-stationaryprocess.estimates ofthesecond-orderstatisticsandcomputationsofthepredictor
coefficientsneedtnbecontinuallyupdated. ‘l'heptoblemofpredictmgatime-acrieswlthout

prior knowledge of its statistics is called adaptive prediction (Friedlander. 1982a).

90

Whenmesecondcordersnusfiaofdeproceubdngpredimedamhnwnesfimanonofdn

leastaquarespredictorisawelldefinedproblem. Awelldefinedproblemisalsopoasibioforthe
enimadonofbansquaresprediedmpammecrswhmandnmfmmadonmmishmwnabom

theprocesaisafinitammberofdatapoiras.(y(n)}wherea-l.2....N.‘l‘hepob1emaadefinedin

W(l981)hwfitfluobnrveddmmammbymm

coefficients.é;.thatminimiaethesumofthesquaredpredictionenors.

SSE I “$901 ).

etn)-y(n)+‘géry(n-i).

(L7)

finenhnnesofmecoefficiennuegivenbyunhomogenemummmmUeequafiommM).

p

e(l)

eth)

 

 

 

q

)‘(1)

rd!)

 

 

31(0) 0
yto)

y(1~i-1) . . yeti-M)

 

 

J

9'.

 

(L8)

 

91

(L8) can bemove compactly written as

 

 

 

 

 

 

c I) +Yé. (L9)
when
P s q
:0) )0)
c . . y I- .
e(}V) 3W)
. . L a
P 7
N0) 0
. . Gt
Y- I ' y(0) . and 6- I .
I I 6.
y(N-l) . . y(N-M) ‘

 

 

The solution of (L8) is given by
9 - K'Wry. (L10)
where YT isthe transpose on and A‘ isthc sample oovuimoenmrix.
R‘srTr (L1!)

The equations that provide the solution to the problem of estimating the predictor coefficients of
apmocss withunlmown statisficshasthcsamc form astlnYule-Wflkoteqnafimwhidtwae

dcn'vcd for process with known statistic: (Friedlander. 19823).

92

There are a number of efficient computational pmoedmes for solving these equations. The
adaptive least square: lattice filter used by Byme and Siegel (1985) is an example. The useful-
mssofannlafiondfipbemeenARmoddhmmadepdvelhwpmdicfimwinbeiWin

Appendibeyshowinghowthisrelationshiphnbeenundintheanalysisofspeeehpmwesee.

 

ILLUSTRATING THE USE OF ADAPTIVE LINEAR PREDICTION TO
EXTRACT IMPULSES FROM PROCESSES
USING SPEECH PROCESSES AS AN EXAMPLE

Asimplifiedmodelforwdtptoductionismownlnfimul. Wmdelccnsistsofan
all-polemwrmatisexdwdbyeimersquasi-paiodicminofimptlsesonwlfitembem
(Malthoul. 1975). Voiced sounds such as vowels are generated flout nearly periodic impulse
sources. meirnpulsetrainrepresentsaseriesofpitdtpulses. Theimpulsesuewdtsfun-
damentalperiodhtownssthepitchperiod. mwltiteprowssproducesthemvoicedsottnds
suchasthefinfish. Tupmbabifitydisuibufimofthewhiteprocessdoesmuppeutobecnti-
calCHaykin. 1984. chap. 1). Them-pole filterrnodelsthevocsltnct. Theidentity ofdnumd
produced by both sourcesis determined bythepameters of the all-pole mteerhoul. 197$).

Inspecchrecognitionandsynthesis.itisofintetcsttodetetminethednnctcroftheindivi-
dualsoundsthatmalteupaSpeechprocess. Ifdnabovcmodelithhetypeofinputsource
that produces the sound must be known. For voiced sound. the pitch period ofthe impulse tnin
must be determined. The parameters of the all-pole filter no needed for both voiced md
unvoiced sounds. Therefore. the objecrives in analyzing a speech process is to estimate the

model parameters and recover the input process.

93

.8858... 58... 3. .82.. 3.32.. .o 5...... .8... .2 8.5.”.

 

 

 

 

 

 

6.38 332::
8. 8.39
.5... .9288
as» 8...: 223
.95. 38>
82.. a8>
58.. till, 9.. ”5.252 tlllll
38: m 8...". 22.-....

 

 

 

 

65.8 32.5
E .6. 8.39

3.8980
5:... 8.2.5.

 

 

 

 

v3.0.— ..85 fl

95

Linearpredictionisusedinthe analysis ofspeechprocesses. Pameterestimationper-
formed through least squares linearpredictionworkswell providedtheirputntheall-polesys-
tern isazeromeanwhiteprocess. lirearpredictioncatbeusedmdeccnvolveaplmtlmis
thcoutputotanall-pole filterthathasbeenexcitedbyawhieproceas. Thewhiteexcitationpro-
cess is recoverable from thepredicticnerror. Fortheamlysisofmdsproducedbyawln'te
input. the constraints on the useofleastsquareelinearpedicticnpleseunoprohlem. Bathe
pcriodicirnpulse sourcethatgeneratesvoicedsoundsisnotwhite. Estimacsofmodelparame-
ters may be biased and deconvolution may be imperfect for non-white inpm prom For
example. ifan input is coherent. the input may not be recoverable from the prediction error. The
model parameters would absorbtheconelarion informationofthsinputprocess. ‘l'heleast
squareslinearpredictorwould produceasnearlyaspossibleawhitepredicticnenorsequence.

lfutemn-whitehtptuishmmmenitispossiblemmmeesdmaeofdnmodd
parameters (Friedlander. 1981). In speech analysis. the input to tie all-pole model may not be
known apricri. In certain situatiom. it may be possible to estimau a non-white input from the
prediction error sequence. In particular. this may be true for the case where the input is an
impulse train as in men processes (Friedlander. 1981).

lrnaginethatanall-pole filtercflmownparameterswasexcitedbyasingleimpulse. A
linear predicror with a configuration that inverses the operation of the all-pole filterwwld be able
to perfectly predict the impulse response of the all-pole filter except forthe first non-zero value of
the response (see FigureMZ). This initial maerovalue wouldshowupinthepredictionerror
(Makhoul, 1975). Similarly, a large prediction error is a good indicator of the occunence of at
impulse exciting the all-pole speechmodel.

Imagine that the configuration ofthe above all-pole filter was not known. The parameters
of the all-pole filter may be obtained from the impulse reSponse of the filter. The parameters of

an unknown all-pole filter can be estimated when the autoconelation coefficients are known for

96

.3323...— 305 3 8.... 0.2— :a 5 he 8:88.. 8.3.5 on. no 5.332.300 d2 2.3...—

Eo-oga boa—P..— 0—£-_—<

 

 

 

eem 8.3.3...
All] 33.8... as...

 

3:83: 339:—

 

 

 

 

 

 

..8=...— 88.:

 

.3... 8.2.5.

‘l

 

 

on.

 

97

theoutputofanallpolcfilterexcitcdbyawtdteproceu. mtmsmmunuu-
quMpfinkingdeamocmrdadmcoefficiandmemofnan-pdemuuemamebr
boththeinputofasingleimpulsecrawhitepocesa. Thisresultisexpectedbecausebotha
determirusdcimpulaeandawhitenoisepmcesshaveidanicallyfiaapecu-a. mm
“mnemomnamummamaamctmmmmmmn
showninthemodelingthespeechprm

Itmigluappeumlfinpitchpuhesofaspeechmcufldbebcandbympedicfim
enors.butthereatesomeproblemswiththismethod. Asignalimpulaelsancnconelatedpro-
cesswemumimpulnuainhmmmfinearwedicfimafimmofnuspeechprm
maybebiased. mumpmdiaormaynctperfecuydeconvolvethespeechprmmpmb-
lemhasbeensnidiedintheateaofspeechanalysis. Friedlander(l981)showshowapanicular
fimupndiaoraleansquaruhnicefiltmcanbemodifiednnhfimiapediaimmnm
biasedwlmthelinearpredictorisusedtodecmvclvedeompmofanafl—polefilterthathasbeen
excitedbyanimpulsetrain.

Anouerpmblemmmlyingonuepresmceofhrgepredicficnmmindicaemelocr
donofpimhpulsemaspeechpmmismmuesymmmmspachpmcenmbe
minimumphase. man-mummoranspeecumoddmmoriuporamemmm
unitcircle. Iflinearpredictionisusedtoinversetheoperationofasystemthatisnotminimum

phase. the prediction error will probably not resemble the process that excited the system.

APPENDIXN

THE UNNORMALIZED PRE-WINDOWED LEAST SQUARES LATTICE FILTER

1heUmrormalizedPre-W‘mdowed1east8quaresuttice Filteristhesame adaptiveleast
squueshnicefilterusedbyLeemdMorf(l980)inmeirpitchpulsedetector. Theleastsquares
laniceflgondmkbasedonuelevuuonobummmcurfiwmedmdofcmnpufingdewlufimm
the Yule-Walker equations. The Yule-Walker equations provide a solution to the problem'of
estimating linear prediction coefficients for processes with known statistics. I-Iayitin (1984).
Friedlander (1982a). and Lee. Mort. and Friedlander (1981) show how the least squares lattice
filter is derived by applying the WW method to the problem of estimating linear
prediction coefficients for processes with unknown statistics. Pre-windowed implies that it was
asnunedthattheinputprowssestothelatticefilterisaempriortot-O. Theprocedureof
esfimafinghmpmdicfimweffidausforpmcessaldmmumwnmfisficshmaflydmeby
minimizingthesumofthesquaredpredicficnenorsmdiscanedleestsquareslimarpredicdcn

Operating on a process with linear prediction can be viewed a being the same as passing
urepmcessUuoughanfiruteimpulseresponsem)filteroran-aerofilter. ‘l‘hecutputot'the
filteristhepredicuonerror. ltisusuallyassurnedthatalinearpredictorisirnplemeruedinthe
direct (or tapped-delay-line) form (Friedlander. 1982a). Figure Ni shows a direct realization of a

least squares linear predictor. The direct realization coefficients. A.- 's. are estimated by the é's of

In;

2...."—
.—z

a

.8.

:8.

he... 5 3 ea...»

.89. 2

8.3.8

has.

.3662.—

 

 

 

 

 

 

 

 

 

 

 

 

 

TN

 

 

 

 

 

a<

 

 

 

 

 

 

TN

 

 

 

 

 

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.<

 

 

 

 

i

1m

c333 88: 33...! a8. 2 .38 5 B .8318. 831. .«z 23E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.59

 

 

 

 

 

 

 

 

 

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101

(L8). Theé'samfinsolufiomwfiteleansquuesfimupredicfionprobianforprmwim
unitnownstatistics. ThestrucnneoftheUmormalizedPre-windowedleastSquaresLattice
Friterisshowninl-‘rgureNZ 1hexr'softhelatticeimplementationarscanedmerefiecn'on
coefficients. Appendingivesdteaigcddlndtatisusedmupdatefiaepuamemrscfunlafice
filter. mdimamafizadonofdeieansqumfinarpredicmrmdmeleansqtmeslamcefim
aremathernatically equivalent. Values fordredirectrealintiatcoefficientscmthederivedfiom
thelattice parameters. Appendingivesmalgoritllnthatcanbeusedtocalculatethedirect

form coefficients from the lattice parameters.

Althoughthedirectformandthelattice formoftheleastsquareslinearpredicmrare
mathematicallyequivalent.tledifferencesintheirstructuresmaygiveoneformaclearadvan-
tageovertheorherinaspecificuse. AusefulpropertyofthelatticeformisthattheMthorder
leastsquareslattice filtercontainswithinitsstructurealllowerorderpedictors. Thepthcrder
lattieefiltercanbeobtainedfromthefirstpsectionsofathhorderlatticestrucmre. Whena
process is filtered with an Mth order lattice filter. the prediction errors and lattice paramemrs of
alllowerorderlatticefiltersareavailable. 'I'hispropettyismtsharedhythedirectrealizaticnof
deleasrsquareslinearpredictor. Separatedirectformsareneededifitisdesiredmsimultane-
ously perform linear predictiononaprocesswithdifferent orders of linearpredictors. Simultane—
ous access to different order linear predictor results may beusefitl inthereal-time analysisof AR

processes with unknown order.

When compared with ether adaptive linear predicrors. the lattice form gives the Pre-
Windowed Least Squares Lattice Filter computational advantages. Friedlander (l982a) divides
adaptive processing methods into to categories: block processing and reclusive teclmiques. The
Pre-Windowed Least Squares Lattice filter has a recursive parameter update algorithm. In block
processing. incoming data are divided into blocks which are then umd to estimate the prediction

parameters. Block processing techniques update parameter estimation only once during a block

102

period. mmcunivetedmiquempredicmrpamnaeresdmamsueupdawdwimeverynewdaa
Therecursivealgorithmmaybemuchmoresensifivetoehangeshtthehrpmprowssmatitneeds
toadaptto.

ApardcuhrfeammofduPre-WlndowedleanSquruuniceFfitermmemancainabiL
itywadaptmchangesinmmpmpmcessismeexponumalweighfingfactorJ. Inmostappli.
cation. the statistics of a process are slowly time-varying (Friedlander. 1982a). Because the
hwprediaorpamnemdeperflmmofflemfisficsofdehnommgmhis
necessaryforthelinearpredictortobeabletotracktimevariationsinthestatisticsofincoming
proceses. ldewrmmesuecharaaerofmexponumalwindowmatdefinesunsaofpastmpm
datausedtoestimatethestatisticsoftheinputprocems. 'Ihevalueofldeterminestheshape
andlcngthoftheexponential window. Olderdatasampleshavelessweightthannewerdatasam-
plesintheestimationofprocessstatistics. ‘l'heexponentialweightingfactoraidsthelatticefilter
inadaptingtonewtrendsintheinputprocessbyallowingittoforgetpatdatavalues. FigureN3
fliusnatesmechamcterofmeexponenfialwhadowforvariousvaluesofk

Anotherimportant feature ofthePre-W'urdowedleastSquaresLattice Filteristhelilteli-
hoodvariablh‘h-I wherenrepresentstheorderofmesecfionmelikelihoodvariabieisbeing
caiculatedforandTrepresemstime. ‘I'helilteiihoodvariabieenablesthelatticefiltertoadapt
quickiytosuddenchangesintheinputprocess. ‘I'heliltelihoodvariableiscimeiyrelatedtothe
log-likelihood function of the lattice filterinputprocess. LeeandMorf (1980) definedthisrela-
tionship in the following way.

Asstnnethat{y,}isazeromean6aussianprocess. 'l'hejcintdistributionfor

pm. . . . 'yT-l). Ian. l-“cl‘”bf. ”' 57-01304”. H. JG-carl (N1)

where

103

A be 8...: 33...... 8.. 33...; 32.2.83 .2... 8...: ge.! 83. 9.. Co 88835 .mz 2.6...—

91585.82..ng

a can 8... 9.... 8m:
.

 

 

 

in...»
I n... 8.5

unan—

 

 

 

104
R. '5b‘r. Jr-al'b‘r. J‘r-al. (N2)

111elog~likelihoodfimctionassociatedwith€hl2)isptoportionalto
L-ian.|+Lyr, Walk-"Ur. Jr-ar- (N3)

hehkefiimodvanaNecanbemMpraedasdempleesfimaeofdesecautummfielog-
likelihood expression of (N3)(Leedc Morf. 1980). ’I'heliltelihoodvariable.'f.: isameasureof
dunkefihoodmusuccessivedauumpleswmcomefiommeameGaussiandimihmmaee
a Morf. 1980). The likelihood variable is a gooddmction statistic ofthe 'unexpectedneas' of
themostrecentinputdatapointsGriedlanderJ982a). ’I'hevalueofy.;rangesfrom0tol.Lee
mdModmponedthatwhuevernm—Gausdmtypecompmmuepresaumdndmnx
tendstolargevalues(closetol). fl‘hefactor(l-7.;)ishrdiederrontinatorofagainusedintlte.
updaterecursionsforcertainlatticeparameters(seeAppendixE). Asy.;approachesl.thegain
goesto-o. ThegainutablesmehfiicefiltermqinckiyadaptmmtexpecteddauaeeaMorf.
1980).
unlikefihoodVMddeduemdMod(1980)mmdemcfimofpimhptnmsmspeedi
processes. WrbasicasmmpfimdeespaechdfiMgpmwssconsimofanappmxi-
mately Gaussian pan (for unvoiced spwch) and a jump component (for voiced speech). Large
firespmdicdmemsangoodmdiafionsofthepresenceofafimpwmporemmpimhpulse
locationintheexcitationprocesses. LeeandMorffoundthatthelocatingpitchpulsesfiompred~
icfimerrorscmldbedonemomaccmatelyifdefikelihoodvanablewasused. Largechmgesin
thelikelihoodvariable correspondedtotheoccunenwsofpitchpulsesinthemchprocess. Lee
andMorfsinwedhowdedmivafiveoffiefikdfinodvanablecwldbeusednamaskmde
extractionofthepitchpuisesfromthepredictionenorsequence.1'helikelihoodvariablewas
usedtosepuammeGaussimcomponamfiomdeiugmymn-Gaussianjumpcompmuusofde

speech driving processes. Byme and Siegel (1985) directly applied the Lee and Morf technique

105

murepmblemofrecovedngheutbeatimpulsesfiommemiaowavemeamremems

AmrmuizedversionofdePre-WindowedLeaaSquuesIatucechrcnbefioundm
Friedlander (1982a). The normalizadon oftheleastsquareslattice algoritlln assuresthatdae
absolutevaluesofthelatticefilm'soutputandparametersareleammorequaitotmity. One
advantageofusingthenonnalizedleastsquareslatticefilteristhatitiseaiertohuildarobust
lmplementationofthefilterwhenflaermgeofthefilter'sparameserauekmwnforeverypusible
operatingcondition. Ammeradvmuagehthatfitenormalizedversionofmelatficefilterisless
complexthantheurmormaiizedversion. Ahernonnalization.thereareonlytlueevariablesinthe
lattice filter parameter update equations. The unnormalized lattice filter has six variables (Fried-
lander.l982a).

Aposdbkdkadvmgehusingdemafizedlaficefilmrkmndepredicfimmam
normalized. Mmaybeapmblemumewuuymgmrecoverdteenctexcimionpmceasthat
wasusedtosynthesistheprocessunderanaiysis. Friedlander(l982a)sbwshowtlmunnormal~
izedhtdceflmrpammemnmdoutpmcanbecalcflamdfiomdepanmemofmemahnd

lattice filter.

REFERENCES

REFERENCES

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