BSPII Ch3 Filtering Time 2008

7/31/2019 BSPII Ch3 Filtering Time 2008

1/15

1

11

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


2/15


3/15

3


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


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..


4/15

4


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


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


5/15

5


ExampleExample:: VisualVisual ERPsERPs

Averaging over10 repetitions

Averaging over20 repetitions


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!)


6/15

6


ExampleExample:: NoisyNoisy ECGECG signalsignal

TwoTwo ECGECG cyclescyclesextractedextracted usingusing triggertrigger

pointspoints fromfrom crosscross--

correlationcorrelation functionfunction

SynchronizedSynchronized averagingaveragingperformedperformed

1111 cyclescycles averagedaveraged


Problem:Problem:

ProposePropose a timea time--domaindomain techniquetechnique totoremoveremove randomrandom noisenoise givengiven onlyonly oneone

realizationrealization ofofthethe signalsignal ororeventevent ofofinterestinterest..


7/15

7


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


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


8/15

8


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


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]]


9/15

9


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


MovingMoving averageaverage filterfilter(8(8--pointpoint))

H(w) = (1/8) exp(-jwk) =(1/8) [1+ exp(-j4w) {1+2cosw+2cos2w+2cos3w}]


10/15

10


IllustrationIllustration ofofapplicationapplication::FilteringFiltering withwith 88--pointpoint MAMA


ProblemProblem

DevelopDevelop a timea time--domaindomain techniquetechnique totoremoveremove basebase--lineline driftdrift inin thethe ECGECG signalsignal


11/15

11


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


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


12/15


13/15


14/15

14


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


MagnitudeMagnitude andand phasephase responseresponse


15/15


RemovalRemoval ofofwanderwander

BSPII Ch3 Filtering Time 2008

Documents

Transcript of BSPII Ch3 Filtering Time 2008