1、2022-8-412022-8-422022-8-43()x n()h n()y nFIR-h(n)finite lengthIIR-h(n)infinite lengthRecursivelyNon-recursively01()()()NNiiiiy na x nib y ni 10Ni)in(x)i(h)n(y NnnH zh n z10 NkkiMkkizbza)z(H101Digital FilterDifferent methods to design IIR filter and FIR filter!2022-8-44.2022-8-45)(jjje|)e(H|)e(H pha
2、se-frequencyAmplitude-frequencyAttenuation of frequency componentsDelay of frequency components Transition|)e(H|lg|)e(H|lgspjsjp 2020 dBp3 c 3dB passband cutoff frequencyPass bandStop band2022-8-46 NiiMiiNiiiMiii)zd()zc(Azbza)z(H111100111 2022-8-472022-8-48 NiiMiiNiiiMiiizdzcAzbzazH111100)1()1(1)()e
3、(Hjw Mijwdjw|)e(H|)e(H|12 2022-8-49;2022-8-410 RequirementHa(s)2022-8-4112022-8-4122022-8-413Impulse invariant(Time domain)1.Transformation Approximate impulse response ha(t)of analog filter using unit impulse response h(n)of digital filter.Let h(n)equal to ha(t)s sampling value,that is:h(n)=ha(t)|t
4、=nT If transfer function of analog filter is Ha(s),then transfer function of required digital filter is:H(z)=ZTL-1(Ha(s)|t=nT2022-8-4141.变换思想变换思想 Impulse Invariant Method使数字滤波器的单位脉冲响应序列使数字滤波器的单位脉冲响应序列h(n)模仿模拟滤波器的冲激响应模仿模拟滤波器的冲激响应ha(t)。aht ah nhnT aHs axt ayt H z x n y nAnalog filterDigital filteraHjA
5、nalog frequency responsejH e Digital frequency response2022-8-415()aHs()H zis Te2 数字化设计过程数字化设计过程1()()iNs taiih tAe u t1()()()iNs nTaiih nh nTAeu nT1NiiiAssInverse Laplacez-transformis111iNis TiAezT2022-8-416 aHs ahtahnT h n aHs H z()()snTanHsh nT e1()()NniH zh n z12()()aamHsHsjmTT sTzePeriodic copie
6、s3.s平面到平面到z平面映射平面映射 Mapping from s-plane to z-planeSampling aHs沿虚轴周期延拓之后沿虚轴周期延拓之后，使用使用 映射到映射到z平面平面sTze H z2022-8-417()sTjjTTj Tzereeee=Tre T 2022-8-4183 数字滤波器与模拟滤波器频响关系数字滤波器与模拟滤波器频响关系若若AF的频响是带限的，且的频响是带限的，且:T|,)j(Ha 0此时此时DF的频响才能不失真重现的频响才能不失真重现AF频响。频响。T ahtahnT h n()12()jamH eHjjmTTT aHj2022-8-4193 数字
7、滤波器与模拟滤波器频响关系数字滤波器与模拟滤波器频响关系实际模拟滤波器的频响是非带限的实际模拟滤波器的频响是非带限的 频谱混叠（该方法严重的缺点）频谱混叠（该方法严重的缺点）适用范围适用范围：低通，带通。：低通，带通。周期延拓周期延拓周期延拓以后，混叠严重，难以转换到数字域周期延拓以后，混叠严重，难以转换到数字域!高通模拟滤波器高通模拟滤波器2022-8-420 TT ,2022-8-421 js)s(Ha，111 js)s(Ha，TtanT1212 001从从时，时，从从TT Tangent transformationT j2022-8-422Image of left half plan
8、eMapping of the s-plane into the z-plane112 11s Ts TesTe 11112 zzTsTsez1 sTsTz22Bilinear transformation112)()(zzTsasHzHs planes1 planez plane2022-8-423 2122121tanTTtanTzss12022-8-424Frequency nonlinear change of bilinear transformation2022-8-425 can be revised by prewarping method.2022-8-426(1)Speci
9、fication(2)Transformation：digital analog Impulse invariance：=T Bilinear transformation(3)Analog filter design(4)Analog filter Digital filter 212tanT)z(H)s(Ha2022-8-42712211210.067450.13490.06745()()1 1.1430.4128sazsT zzzH zHszz:100Hz,300Hz,1000HzpssDFffF3dB,20dBps0.2,0.6,ps2tan(/2)685.82109(Hz)2tan(
10、/2)2452.762438(Hz)ppssssTT ,psps2022-8-428 LowpassHighpassBandpassBandstop2022-8-429 aHs H z zf s aHs 1Hz zf s 2HZ)Z(gz11 2022-8-43011112 zzTs0101splane originzsjz ，2 ctg2022-8-4312022-8-43200000 1jsplane originzesjz ，sincoscoszcoszzzzezezsjj 020211211002022-8-433 00000 ，coscossincoszzzs 00221212022
11、-8-434 )Z(gz11 2022-8-4352022-8-4362022-8-437Digital filter specificationAnalog filter specificationAnalog low-pass prototypeAnalog frequency transformDigital lowpass prototypeAnalog/digital transformDigital/digital frequency transformDigital filters system function(1)(2)2022-8-438Review1.Approach t
12、o IIR design (1)(2)(3)Design digital filter with analog filter(mapping)Must meets two conditions：Frequency response simulation:j on unit circle Casual and stability invariable:left half on s-plane unit circle2022-8-4392.Approach to IIR filter design(1)Impulse invariance Application of sampling theor
13、em(time-domain)Transform:Linear frequency mapping Frequency aliasing Applicable to lowpass filter and bandpass filter(2)Bilinear transformations plane z plane(frequency domain)Transform pair:Non-linear frequency mappingDesign Simply.(3)Prototype transformPrototype:Lowpass analog filter Other types of filterThree types:Analog lowpass AF LP,HP,BP,BS DF Analog lowpass DF LP,HP,BP,BS Analog lowpass DF LP DF LP,HP,BP,BS
