模仿模拟滤波器的冲激响应hatAnalogfilterDigitalfilterAnalog课件.ppt

1、2022-12-2512022-12-2522022-12-253()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!2022-12-254.2022-12-255)(jjje|)e(

2、H|)e(H phase-frequencyAmplitude-frequencyAttenuation of frequency componentsDelay of frequency components Transition|)e(H|lg|)e(H|lgspjsjp 2020 dBp3 c 3dB passband cutoff frequencyPass bandStop band2022-12-256 NiiMiiNiiiMiii)zd()zc(Azbza)z(H111100111 2022-12-2572022-12-258 NiiMiiNiiiMiiizdzcAzbzazH1

3、11100)1()1(1)()e(Hjw Mijwdjw|)e(H|)e(H|12 2022-12-259;2022-12-2510 RequirementHa(s)2022-12-25112022-12-25122022-12-2513Impulse 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

4、value,that is:h(n)=ha(t)|t=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=nT2022-12-25141.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 nAna

5、log filterDigital filteraHjAnalog frequency responsejH e Digital frequency response2022-12-2515()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 TiAezT2022-12-2516 aHs ahtahnT h n aHs H z()()snTanHsh nT e1()()NniH zh n z12()

6、()aamHsHsjmTT sTzePeriodic copies3.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 z2022-12-2517()sTjjTTj Tzereeee=Tre T 2022-12-25183 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(

7、)12()jamH eHjjmTTT aHj2022-12-25193 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2022-12-2520 TT ,2022-12-2521 js)s(Ha，111 js)s(Ha，TtanT1212 001从从时，时，从从TT Tangent transfor

8、mationT j2022-12-2522Image of left half planeMapping of the s-plane into the z-plane112 11s Ts TesTe 11112 zzTsTsez1 sTsTz22Bilinear transformation112)()(zzTsasHzHs planes1 planez plane2022-12-2523 2122121tanTTtanTzss12022-12-2524Frequency nonlinear change of bilinear transformation2022-12-2525 can

9、be revised by prewarping method.2022-12-2526(1)Specification(2)Transformation：digital analog Impulse invariance：=T Bilinear transformation(3)Analog filter design(4)Analog filter Digital filter 212tanT)z(H)s(Ha2022-12-252712211210.067450.13490.06745()()1 1.1430.4128sazsT zzzH zHszz:100Hz,300Hz,1000Hz

10、pssDFffF3dB,20dBps0.2,0.6,ps2tan(/2)685.82109(Hz)2tan(/2)2452.762438(Hz)ppssssTT ,psps2022-12-2528 LowpassHighpassBandpassBandstop2022-12-2529 aHs H z zf s aHs 1Hz zf s 2HZ)Z(gz11 2022-12-253011112 zzTs0101splane originzsjz ，2 ctg2022-12-25312022-12-253200000 1jsplane originzesjz ，sincoscoszcoszzzze

11、zezsjj 020211211002022-12-2533 00000 ，coscossincoszzzs 00221212022-12-2534 )Z(gz11 2022-12-25352022-12-25362022-12-2537Digital filter specificationAnalog filter specificationAnalog low-pass prototypeAnalog frequency transformDigital lowpass prototypeAnalog/digital transformDigital/digital frequency

12、transformDigital filters system function(1)(2)2022-12-2538Review1.Approach to 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 circle2022-12-25392.Ap

13、proach to IIR filter design(1)Impulse invariance Application of sampling theorem(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