CHAPTER 7 filter design techniques 7.0 introduction 7.Idesign of discrete-time IIR filters from continuous-time filters filter design by impuls e invariance 7.1.2 filter design by bilinear transform 7.1.3 not low pass filter design and other method 7.2 design of Fir filters by windowing 7.3 summary
7.0 introduction 7.1design of discrete-time IIR filters from continuous-time filters 7.1.1 filter design by impulse invariance 7.1.2 filter design by bilinear transform 7.1.3 not low pass filter design and other method 7.2 design of FIR filters by windowing. 7.3 summary CHAPTER 7 filter design techniques
7.0 introduction ideal frequency selective filter 2其-c2Ⅱ c 2 (a)理想低通 (b)理想高通 H(eJ° C 2其 2 (c)理想带通 (①理想带隕 band-stop filter: notch filter; quality factor of band-pass filter=pass-band width/ center frequency
7.0 introduction ideal frequency selective filter band-stop filter：notch filter；quality factor of band-pass filter=pass-band width/center frequency
CD H(e D/C r, (t yIn ya(t) Figure 7.1 impulse response of ideal low-pass filter, noncausal, unrealizable sin(on) ha(n) Oc h dle Jo dOn O 丌J- Specifications for filter design given in frequency domain pl ase: inear magnitude: given by a tolerance scheme analog or digital, absolute or relative
Figure 7.1 = = = − − , ...... sin( ) ( ) 2 1 ( ) n n n h n H e e d j j n c d d c c impulse response of ideal low-pass filter，noncausal，unrealizable Specifications for filter design ：given in frequency domain phase：linear? magnitude：given by a tolerance scheme analog or digital，absolute or relative
Hefr(in2) absolute specification 1+δ magnitude response of equivalent analog system Passband i Transition Stopband δ He/) 1+δ 3dB cutoff Passband i Transition Stopband stope Figure 7. toleranc monotonous\ descent T toft -Feetenev
Figure 7.2 magnitude response of equivalent analog system monotonous descent 1/ 2 c passband tolerance c stopband tolerance passband cutoff frequency stopband cutoff frequency 3dB cutoff frequency absolute specification
relative specifications: maximum magnitude in passband is normalized to l, viz. odB 20*log10(1 0 maximum attenuation in passband 20*log106>0 minimum attenuation in stopband BdB cutoff frequency: H(e/)=l/√2 20log1o H(ec)=3dB magnitude response of equivalent analog system H(eJo)l Heff(jQ2) T } T digital specification, finally: @p=Qp 1, as=Q25T
relative specifications：maximum magnitude in passband is normalized to 1, viz. 0dB 20*log 0 20*log 1 0 10 10 = − = − − s s p p （ ） maximum attenuation in passband minimum attenuation in stopband 3dB cutoff frequency： H e dB H e c c j j 20log | ( ) | 3 | ( ) | 1/ 2 − 10 = = p = p T,s = s T = = T T H e H j T j eff 0 | | ( ) | | | ( ) magnitude response of equivalent analog system: digital specification, finally: