音频去噪 Enhancing Speech by removing noise.docx
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音频去噪 Enhancing Speech by removing noise.docx
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音频去噪EnhancingSpeechbyremovingnoise
Laboratory5
EnhancingSpeechbyremovingnoise
Purpose
ThemainpurposeofthislabistodesigndifferentIIRandFIRfiltersinthecontextofenhancingapeechcorruptedbyanadditivenoise.Bydoingso,thiswillhelpustobetterunderstandthepropertiesofdifferenttypesoffilters,themeaningsofthedesignparameters,andsomeofthetrade‐offsbetweenfilterclasses.
Inordertoseethebehaviorofthesedifferenttypesoffilters,weweregivenanoisyspeechsignalandwereaskedtodesignalow-passfilterinordertoremovethehigh-passnoise.Afterdoingthis,wehadtopasstheaudiofilethrougheachofthesefiltersinordertoseetheifthespeechwasfilteredcorrectlyandwhatistheeffectofeachfilteronthefilteredsignal.ThenoisysignalwassampledatafrequencyFs=44100Hzandthefilterspecificationsare:
PartI :
MatlabRipple
PartII:
Butterworthfilter
Inthispart,wehadtodesignaButterworthfilterthatsatisfiesthegivenspecifications.WeusedMatlabfdatooltodesignthisfilter.InordertousethisMatlabbuilt-intool,wehadtoconverttheabovegivenspecificationsintoIIRfilterspecifications.Thus,wetook:
Apass=Gpbmax–Gpbmin=40–37=3dB
Astop=Gpbmax–Gsbmax=40-(-55)=95dB
AsforFpass,FstopandFs,weput2500Hz,4000Hzand44100Hzrespectively.
Afterdesigningthisfilter,wefoundbyusingtheMatlab‘’order’’functionthatthetheorderofthisfilteris23.
Thenextstepwastodeterminethenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilter.Inordertodothis,weusedtheMatlab‘’cost’’functionandfoundthatthenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilteris46.
WealsohadtoplotthemagnituderesponseofthisfilterindBandinlinearscalealongwiththegroupdelay.Figure1showsthecorrespondingresults.
Figure1–MagnitudeandgroupdelayoftheButterworthfilter
Afterplottingthemagnitudeandgroupdelayofthisfilter,wehadtoplotthepole-zerodiagram.Figure2showsthecorrespondingresult.
Figure2–Pole-zeroplotoftheButterworthfilter
Anotherimportantaspectofthefilterthatwehavetoconsideristheimpulseresponse.UsingtheMatlab‘’filter’’and‘’stem’’functions,weplottedtheimpulseresponseifthisfilter.Figure3showsthecorrespondingresult.
Figure3–ImpulseresponseoftheButterworthfilter
Finally,wefilteredthenoisysignalwiththisfilterandnoticedthatthenoisewasalmostcompletelyremovedandthatwecanlistenclearlytothespeechwithoutanynoise.However,thefilteredsignalwasnotstrongenoughandneededtobeamplifiedenorderforthesoundtobeloudenough.Soweamplifiedthefilteredsignalbyafactorof100andnoticedthatthespeechwasloudenoughandveryclear.
PartIII:
ChebyshevTypeIfilter
Inthispart,wehadtodesignaChebyshevTypeIfilterthatsatisfiesthegivenspecifications.WeusedMatlabfdatooltodesignthisfilter.InordertousethisMatlabbuilt-intool,wehadtoconverttheabovegivenspecificationsintoIIRfilterspecifications.Thus,wetookthesameparametersasweusedwiththeButterworthfilter:
Apass=Gpbmax–Gpbmin=40–37=3dB
Astop=Gpbmax–Gsbmax=40-(-55)=95dB
AsforFpass,FstopandFs,weput2500Hz,4000Hzand44100Hzrespectively.
Afterdesigningthisfilter,wefoundbyusingtheMatlab‘’order’’functionthatthetheorderofthisfilteris11.
Thenextstepwastodeterminethenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilter.Inordertodothis,weusedtheMatlab‘’cost’’functionandfoundthatthenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilteris22.
WealsohadtoplotthemagnituderesponseofthisfilterindBandinlinearscalealongwiththegroupdelay.Figure4showsthecorrespondingresults.
Figure4–MagnitudeandgroupdelayoftheChebyshevTypeIfilter
Afterplottingthemagnitudeandgroupdelayofthisfilter,wehadtoplotthepole-zerodiagram.Figure5showsthecorrespondingresult.
Figure5–Pole-zeroplotoftheChebyshevTypeIfilter
Anotherimportantaspectofthefilterthatwehavetoconsideristheimpulseresponse.UsingtheMatlab‘’filter’’and‘’stem’’functions,weplottedtheimpulseresponseifthisfilter.Figure6showsthecorrespondingresult.
Figure6–ImpulseresponseoftheChebyshevTypeIfilter
Finally,wefilteredthenoisysignalwiththisfilterandnoticedthatthenoisewasalmostcompletelyremovedandthatwecanlistenclearlytothespeechwithoutanynoise.However,thefilteredsignalwasnotstrongenoughandneededtobeamplifiedenorderforthesoundtobeloudenough.Soweamplifiedthefilteredsignalbyafactorof100andnoticedthatthespeechwasloudenoughandveryclear.
PartIV:
ChebyshevTypeIIfilter
Inthispart,wehadtodesignaChebyshevTypeIIfilterthatsatisfiesthegivenspecifications.WeusedMatlabfdatooltodesignthisfilter.InordertousethisMatlabbuilt-intool,wehadtoconverttheabovegivenspecificationsintoIIRfilterspecifications.Thus,wetookthesameparametersasweusedwiththeButterworthfilter:
Apass=Gpbmax–Gpbmin=40–37=3dB
Astop=Gpbmax–Gsbmax=40-(-55)=95dB
AsforFpass,FstopandFs,weput2500Hz,4000Hzand44100Hzrespectively.
Afterdesigningthisfilter,wefoundbyusingtheMatlab‘’order’’functionthatthetheorderofthisfilteris11.
Thenextstepwastodeterminethenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilter.Inordertodothis,weusedtheMatlab‘’cost’’functionandfoundthatthenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilteris22.
WealsohadtoplotthemagnituderesponseofthisfilterindBandinlinearscalealongwiththegroupdelay.Figure7showsthecorrespondingresults.
Figure7–MagnitudeandgroupdelayoftheChebyshevTypeIIfilter
Afterplottingthemagnitudeandgroupdelayofthisfilter,wehadtoplotthepole-zerodiagram.Figure8showsthecorrespondingresult.
Figure8–Pole-zeroplotoftheChebyshevTypeIIfilter
Anotherimportantaspectofthefilterthatwehavetoconsideristheimpulseresponse.UsingtheMatlab‘’filter’’and‘’stem’’functions,weplottedtheimpulseresponseifthisfilter.Figure9showsthecorrespondingresult.
Figure9–ImpulseresponseoftheChebyshevTypeIIfilter
Finally,wefilteredthenoisysignalwiththisfilterandnoticedthatthenoisewasalmostcompletelyremovedandthatwecanlistenclearlytothespeechwithoutanynoise.However,thefilteredsignalwasnotstrongenoughandneededtobeamplifiedenorderforthesoundtobeloudenough.Soweamplifiedthefilteredsignalbyafactorof100andnoticedthatthespeechwasloudenoughandveryclear.
PartV:
Ellipticfilter
Inthispart,wehadtodesignanEllipticfilterthatsatisfiesthegivenspecifications.WeusedMatlabfdatooltodesignthisfilter.InordertousethisMatlabbuilt-intool,wehadtoconverttheabovegivenspecificationsintoIIRfilterspecifications.Thus,wetookthesameparametersasweusedwiththeButterworthfilter:
Apass=Gpbmax–Gpbmin=40–37=3dB
Astop=Gpbmax–Gsbmax=40-(-55)=95dB
AsforFpass,FstopandFs,weput2500Hz,4000Hzand44100Hzrespectively.
Afterdesigningthisfilter,wefoundbyusingtheMatlab‘’order’’functionthatthetheorderofthisfilteris8.
Thenextstepwastodeterminethenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilter.Inordertodothis,weusedtheMatlab‘’cost’’functionandfoundthatthenumberofmultiplicationoperationsperinputsamplerequiredtoimplementthefilteris16.
WealsohadtoplotthemagnituderesponseofthisfilterindBandinlinearscalealongwiththegroupdelay.Figure10showsthecorrespondingresults.
Figure10–MagnitudeandgroupdelayoftheEllipticfilter
Afterplottingthemagnitudeandgroupdelayofthisfilter,wehadtoplotthepole-zerodiagram.Figure11showsthecorrespondingresult.
Figure11–Pole-zeroplotoftheEllipticfilter
Anotherimportantaspectofthefilterthatwehavetoconsideristheimpulseresponse.UsingtheMatlab‘’filter’’and‘’stem’’functions,weplottedtheimpulseresponseifthisfilter.Figure12showsthecorrespondingresult.
Figure12–ImpulseresponseoftheEllipticfilter
Finally,wefilteredthenoisysignalwiththisfilterandnoticedthatthenoisewasalmostcompletelyremovedandthatwecanlistenclearlytothespeechwithoutanynoise.However,thefilteredsignalwasnotstrongenoughandneededtobeamplifiedenorderforthesoundtobeloudenough.Soweamplifiedthefilteredsignalbyafactorof100andnoticedthatthespeechwasloudenoughandveryclear.
Conclusion
Thepurposeofthisexperimentwastoverifyaconjecturethatstatesthattheearisinsensitivetophase.Inordertodothis,wehadtoimplementall-passfiltersthatwouldkeepthesamemagnitudeofthefrequencyresponseoftheaudiosignalbutwillintroduceaphaseshift.
Bydoingthis,wehadtheopportunitytobetterunderstandsomeconceptsrelatingtoallpassfilters.Wealsosawthebehaviourofthesefilterswhenwehaveanimpulseinput.Also,weplottedthemagnitude,thegroupdelayandthepole-zeroplotoftheall-passfiltersinordertostudythemagnitudeofthefrequencyresponseandthephaseintroducedbyanallpassfilter.Wealsohadtheopportunitytoseetherelationthatexistsbetweenthepolesandzerosinanallpassfiltersandnoticedthat
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