数字信号处理-ch9

Chapter9IIRDigitalFilterDesign•9.1PreliminaryConsiderations•AppendixA.AnalogLowpassFilterDesign•AppendixB.DesignofAnalogHighpass,BandpassandBandstopFilters•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesign•9.1PreliminaryConsiderations•AppendixA.AnalogLowpassFilterDesign•AppendixB.DesignofAnalogHighpass,BandpassandBandstopFilters•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesignA.1A.2A.32|()|aHjWA.4•9.1PreliminaryConsiderations•AppendixA.AnalogLowpassFilterDesign•AppendixB.DesignofAnalogHighpass,BandpassandBandstopFilters•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesignB.1B.2B.3•9.1PreliminaryConsiderations•AppendixA.AnalogLowpassFilterDesign•AppendixB.DesignofAnalogHighpass,BandpassandBandstopFilters•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesign•9.1PreliminaryConsiderations•AppendixA.AnalogLowpassFilterDesign•AppendixB.DesignofAnalogHighpass,BandpassandBandstopFilters•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesign§9.3DesignoflowpassIIRDigitalFilter•Example-DesignalowpassButterworthdigitalfilterwithp=0.25,s=0.55,p=0.5dB,ands=15dBAnalysis:If|G(ej0)|=1thisimplies20log10|G(ej0.25)|-0.520log10|G(ej0.55)|-15§9.3DesignoflowpassIIRDigitalFilter•Solution:Prewarping,weget(makingT=2)p=tan(p/2)=tan(0.25/2)=0.4142136s=tan(s/2)=tan(0.55/2)=1.1708496AnalogfilterDesign22120lg0.50.122018512120lg1531.622777AA§9.3DesignoflowpassIIRDigitalFilterTheinversetransitionratiois1/k=s/p=2.8266809Theinversediscriminationratiois2111/15.841979Ak§9.3DesignoflowpassIIRDigitalFilterChooseN=3Wethengetc=1.419915p=0.588148§9.3DesignoflowpassIIRDigitalFilter3rd-orderlowpassButterworthtransferfunctionforc=1isHan(s’)=1/(s’3+2s’2+2s’+1)Denormalizingtogetc=0.588148wearriveat()()()0.588148aanancssHsHH§9.3DesignoflowpassIIRDigitalFilter•ApplyingbilineartransformationtoHa(s)wegetthedesireddigitaltransferfunction1111)()(zzsasHzGMagnitudeandgainresponsesofG(z)shownbelow:•4.4AnalogLowpassFilterDesign•4.5DesignofAnalogHighpass,BandpassandBandstopFilters•9.1PreliminaryConsiderations•9.2BilinearTransformationMethodofIIRFilterDesign•9.3DesignofLowpassIIRDigitalFilters•9.4DesignofHighpass,Bandpass,andBandstopIIRDigitalFilters•9.5SpectralTransformationsofIIRFiltersChapter9IIRDigitalFilterDesign§9.4IIRHighpass,Bandpass,andBandstopDigitalFilterDesign§9.4IIRHighpass,Bandpass,andBandstopDigitalFilterDesign§9.4IIRHighpass,Bandpass,andBandstopDigitalFilterDesign§9.4IIRHighpass,Bandpass,andBandstopDigitalFilterDesign§9.4.1IIRHighpassDigitalFilterDesign•Example-DesignofaType1ChebyshevIIRdigitalhighpassfilterSpecifications:Fp=700Hz,Fs=500Hz,p=1dB,s=32dB,FT=2kHz•Solution:•Normalizedangularbandedgefrequenciesp=2Fp/FT=2700/2000=0.7rad/samples=2Fs/FT=2500/2000=0.5rad/sample§9.4.1IIRHighpassDigitalFilterDesign•Analoglowpassfilterspecifications:p=1,s=1.926105,p=1dB,s=32dB9626105.1)2/tan(ˆpp0.1)2/tan(ˆss•PrewarpingthesefrequencieswegetFortheprototypeanaloglowpassfilterchoosep=1ˆˆppUsingwegets=1.962105§9.4.1IIRHighpassDigitalFilterDesign•MATLABcodefragmentsusedforthedesign[N,Wn]=cheb1ord(1,1.9626105,1,32,‘s’)[B,A]=cheby1(N,1,Wn,‘s’);[BT,AT]=lp2hp(B,A,1.9626105);[num,den]=bilinear(BT,AT,0.5);§9.4.1IIRHighpassDigitalFilterDesign1122ˆ1ˆˆ1,(4)ˆ()()()pppscpszssszLPHPANHsHsGz•Theprocedureofdesign（supposingit’sabutterworthfilter）§9.4.2IIRBandpassDigitalFilterDesign•Example-DesignofaButterworthIIRdigitalbandpassfilter•Specifications:p1=0.45,p2=0.65,s1=0.3,s2=0.75,p=1dB,s=40dB•Solution:•Prewarpingweget8540807.0)2/tan(ˆ11pp6318517.1)2/tan(ˆ22pp41421356.2)2/tan(ˆ22ss5095254.0)2/tan(ˆ11ss§9.4.2IIRBandpassDigitalFilterDesignFortheprototypeanaloglowpassfilterwechoosep=1393733.1ˆˆˆ212ppo212ˆˆˆ1.23010325sso5773031.0ˆ1s•Weset1ˆs1ˆs2ˆs2ˆo•Wethereforemodifysothatandexhibitgeometricsymmetrywithrespectto777771.0ˆˆ12ppwB•Widthofpassband§9.4.2IIRBandpassDigitalFilterDesign•SpecificationsofprototypeanalogButterworthlowpassfilter:p=1,s=2.3617627,p=1dB,s=40dB3617627.2777771.05773031.03332788.0393733.1swopBˆˆˆ22•Usingweget§9.4.2IIRBandpassD