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ChapterChapter33
TimeTime--domaindomain FilteringFiltering
forforRemovalRemoval ofofArtifactsArtifacts
Dr. BDr. Blent Ylent Ylmazlmaz
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 22
Contents
TimeTime--domain filtersdomain filters SynchronizedSynchronized averagingaveraging
MovingMoving--averageaverage filtersfilters
DerivativeDerivative--basedbased operatorsoperators toto removeremove lowlow--frequencyfrequency artifactsartifacts
Applications: Removal of artifacts in the ECG
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SynchronizedSynchronized averagingaveraging
Linear filters failLinear filters fail When the signal and noise spectra overlapWhen the signal and noise spectra overlap
Synchronized signal averagingSynchronized signal averaging ccan separate aan separate arepetitive signal from noise w/o disturbing the signalrepetitive signal from noise w/o disturbing the signal
AlignmentAlignment of the waveforms is importantof the waveforms is important NoNo frequencyfrequency--domaindomain filteringfiltering isis necessarynecessary
IfIfnoise is random with zero mean andnoise is random with zero mean anduncorrelateduncorrelated with the signalwith the signal aaveragingveraging willwillimprove SNRimprove SNR
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 66
ERP & SEPERP & SEP ERP:ERP: EventEvent--relatedrelated potentialpotential
SEP:SEP: SSoommaattoosseennssoorryy evokedevoked potentialpotential
TheThe somatosensorysomatosensory systemsystem isis thethe sensorysensorysystemsystem ofofsomaticsomatic sensationsensation.. TheThe sense ofsense oftouchtouch isis mediatedmediated byby thethe
somatosensorysomatosensory systemsystem.. TouchTouch maymay simplysimply bebeconsideredconsidered oneone ofoffivefive humanhuman sensessenses;; howeverhowever,, whenwhenaa personperson touchestouches somethingsomething ororsomebodysomebody thisthis givesgivesriserise toto variousvarious feelingsfeelings:: thethe perceptionperception ofofpressurepressure((hencehence shapeshape,, softnesssoftness,, texturetexture,, vibrationvibration,, etcetc.),.),relativerelative temperaturetemperature andand sometimessometimes painpain.. ThusThus thethetermterm ""touchtouch" is" is actuallyactually thethe combinedcombined termterm forforseveralseveralsensessenses.. InIn medicinemedicine,, thethe colloquialcolloquial termterm ""touchtouch" is" isusuallyusually replacedreplaced withwith somaticsomatic sensessenses,, toto betterbetterreflectreflect thethe varietyvariety ofofmechanismsmechanisms involvedinvolved..
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ExamplesExamples::
ERPsERPs andand SEPsSEPs Epochs obtained a number of times by
repeated application of the stimulus
Stimulus is used to align the epochs
Averaging is then performed
ECG signals filtered by detecting the QRS complexes and
their position to align the waveforms
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 88
AlgorithmAlgorithm
M repetitionsM repetitions --> SNR increase by a factor> SNR increase by a factorMM Obtain a number of realizationsObtain a number of realizations Determine a reference pointDetermine a reference point
Trigger if external stimulationTrigger if external stimulation
Repetitive eventsRepetitive events QRS complexes in the ECG or S1 and S2 in the PCGQRS complexes in the ECG or S1 and S2 in the PCG
Extract parts corresponding to events and add themExtract parts corresponding to events and add themto a bufferto a buffer
Divide the results in the buffer by the # of eventsDivide the results in the buffer by the # of eventsaddedadded
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ExampleExample:: VisualVisual ERPsERPs
Averaging over10 repetitions
Averaging over20 repetitions
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1010
ExampleExample:: NoisyNoisy ECGECG signalsignal
Sample QRS complexSample QRS complex First beat used as aFirst beat used as a
template (86 ms)template (86 ms)
Template matchingTemplate matching
Normalized crossNormalized cross--correlationcorrelation
CrossCross--correlation peakscorrelation peaks(value is 1) at the(value is 1) at thelocations of QRSlocations of QRS
Choose an appropriateChoose an appropriatethreshold (be careful!)threshold (be careful!)
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ExampleExample:: NoisyNoisy ECGECG signalsignal
TwoTwo ECGECG cyclescyclesextractedextracted usingusing triggertrigger
pointspoints fromfrom crosscross--
correlationcorrelation functionfunction
SynchronizedSynchronized averagingaveragingperformedperformed
1111 cyclescycles averagedaveraged
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1212
Problem:Problem:
ProposePropose a timea time--domaindomain techniquetechnique totoremoveremove randomrandom noisenoise givengiven onlyonly oneone
realizationrealization ofofthethe signalsignal ororeventevent ofofinterestinterest..
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SolutionSolution:: MovingMoving--averageaverage filtersfilters
TemporalTemporal averagingaveraging forfornoisenoise removalremoval
y[n] =y[n] = bbkk x[nx[n--k]k] bbkk:: filterfiltercoefficientscoefficients, k = 0, k = 0 NN
N:N: orderorderofofthethe filterfilter
TheThe effecteffect ofofdivisiondivision byby thethe numbernumberofof
samplessamples usedused isis includedincluded inin thethe valuesvalues ofoffilterfiltercoefficientscoefficients
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1414
MAFMAF
H(z)=bH(z)=b00+b+b11zz--11+b+b22zz
--22++++bbNNzz--NN
SpecialSpecial MAF:MAF: HanningHanning filterfilter
H(z)=(1/4)[1+2zH(z)=(1/4)[1+2z--11+z+z--22]] DoubleDouble zerozero at z=at z=--11
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AdvantagesAdvantages andand attributesattributes of MAFof MAF
h[k] has ah[k] has a finitefinite numbernumberofoftermsterms FIRFIR filterfilter
NoNo recursionrecursion, no, no feedbackfeedback
TheThe outputoutput dependsdepends onlyonly onon thethe presentpresent inputinputsamplesample andand aa fewfew pastpast inputinput samplessamples
FilterFilteris a set of tapis a set of tap weightsweights ofofthethe delaydelay stagesstages
NoNo polespoles exceptexcept at z=0at z=0
InherentlyInherently stablestable
LinearLinearphasephase SymmetricSymmetric ororantisymmetricantisymmetric taptap weightsweights
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1616
HanningHanning FilterFilter
H(w)=(1/4)[1+2eH(w)=(1/4)[1+2e--jwjw+e+e--j2wj2w]]
H(w)=(1/4)[{2+2cos(w)}eH(w)=(1/4)[{2+2cos(w)}e--jwjw]]
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HanningHanning filterfilter
-- LowpassLowpass filterfilter withwith
linearlinear phasephase
-- MagnitudeMagnitude andand
phasephase responseresponse assistassist
inin undestandingundestanding thethe
effecteffect ofofthethe filterfilter ononthethe frequencyfrequency
componentscomponents ofofthethe
signalsignal andand noisenoise
MagnitudeMagnitude responseresponse = |(1/2){1+= |(1/2){1+coscos(w)}|(w)}|
PhasePhase responseresponse == --ww
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1818
MovingMoving averageaverage filterfilter(8(8--pointpoint))
H(w) = (1/8) exp(-jwk) =(1/8) [1+ exp(-j4w) {1+2cosw+2cos2w+2cos3w}]
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Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 1919
IllustrationIllustration ofofapplicationapplication::FilteringFiltering withwith 88--pointpoint MAMA
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 2020
ProblemProblem
DevelopDevelop a timea time--domaindomain techniquetechnique totoremoveremove basebase--lineline driftdrift inin thethe ECGECG signalsignal
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Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 2121
DerivativeDerivative--basedbased operatorsoperatorstoto removeremove lowlow--frequencyfrequency artifactsartifacts
DerivativeDerivative operatoroperatorin timein time--domaindomain RemovesRemoves partsparts thatthat areare constantconstant
LargeLarge changeschanges inin thethe inputinput -->> highhigh valuesvalues inin
thethe outputoutput
BoostBoost HFHF componentscomponents andand suppresssuppress LFLFcomponentscomponents
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 2222
DerivativeDerivative operatoroperator
d/d/dtdt -->> multiplicationmultiplication bybyjwjw ororj2*pi*fj2*pi*f
GainGain ofofthethe freqfreq responseresponse, H(w)=, H(w)=jwjw
startsstarts withwith 00 andand increasesincreases linearlylinearly SecondSecond--orderorderderivativederivative operatoroperatordd22/dt/dt22
H(w) =H(w) = --ww22
QuadraticQuadratic increaseincrease inin gaingain forforHFHF componentscomponents
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SolutionSolution
ToTo obtainobtain highhigh gaingain inin thethe lowlow frequenciesfrequenciesplaceplace aa polepole onon thethe realreal axisaxis ((zerozero))
frequencyfrequency at z=0.995at z=0.995
H(z)=(1/T)[(1H(z)=(1/T)[(1--zz--11)/(1)/(1--0.995z0.995z--11)])]
H(z)=(1/T)[(zH(z)=(1/T)[(z--1)/(z1)/(z--0.995)]0.995)]
y[n]=(1/T)(x[n]y[n]=(1/T)(x[n]--x[nx[n--1])+0.995y[n1])+0.995y[n--1]1]
pole
Dr. BDr. Blent Ylent Ylmazlmaz BME402:BME402: BiomedicalBiomedical SignalSignal ProcessingProcessing--IIII 2828
MagnitudeMagnitude andand phasephase responseresponse
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RemovalRemoval ofofwanderwander
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