Matlab Implementation Digital Signal Processing--IIR Digital Filter Design Function [b,a]impinvar(c,d,fs) *b=numerator coefficients of digital filter *a denominator coefficients of digital filter *c=numerator coefficients of analog filter *d denominator coefficients of analog filter *fs=sampling frequency H.间=7+5+6 8+1 以0-”62 2T 10-0209z fs=1 阳= 1-e21-e21-01851+00067z3 B=[1,1]; A=[1,5,6]; T=1; Fs=1/T; [Bz,Az]=impinvar (B,A,Fs); result: Bz=1.0000 -0.2209 Az=1.0000 -0.1851 0.0067 上游充通大粤
Matlab Implementation Digital Signal Processing—— IIR Digital Filter Design Function [b,a] = impinvar(c,d,fs) b = numerator coefficients of digital filter a = denominator coefficients of digital filter c = numerator coefficients of analog filter d = denominator coefficients of analog filter fs= sampling frequency fs=1 B=[1,1]; A=[1,5,6]; T=1; Fs=1/T; [Bz,Az]=impinvar(B,A,Fs); result： Bz =1.0000 -0.2209 Az = 1.0000 -0.1851 0.0067
Advantages of Impulse Invariance Mapping NG U Digital Signal Processing--IIR Digital Filter Design It is a stable design and the frequencies and w are linearly related. Disadvantage We should expect some aliasing of the analog frequency response,and in some cases this aliasing is intolerable. Consequently,this design method is useful only when the analog filter is essentially band- limited to a lowpass or bandpass filter in which there are no oscillations in the stopband. 上游充通大￥
Advantages of Impulse Invariance Mapping Digital Signal Processing—— IIR Digital Filter Design It is a stable design and the frequencies Ω and w are linearly related. Disadvantage We should expect some aliasing of the analog frequency response, and in some cases this aliasing is intolerable. Consequently, this design method is useful only when the analog filter is essentially bandlimited to a lowpass or bandpass filter in which there are no oscillations in the stopband
Bilinear Transformation Digital Signal Processing--IIR Digital Filter Design Low pass digital filter to low pass 1-z1 S= analog filter 1+2, tan 2 transform High pass digital 1+z1 filter to low pass analog filter 1-2, 2=-co transform Band pass digital 1-2cz1+z2 C-coSO filter to low pass S= analog filter 1-22 sin transform Band stop digital 1-z2 sin o filter to low pass S三 analog filter 1-2cz1+z2, 2= c-cos@ transform 上游充通大￥
Digital Signal Processing—— IIR Digital Filter Design Bilinear Transformation Low pass digital filter to low pass analog filter transform High pass digital filter to low pass analog filter transform Band pass digital filter to low pass analog filter transform Band stop digital filter to low pass analog filter transform
Bilinear Transformation Digital Signal Processing--IIR Digital Filter Design U UY A ass pass 1 1 1十epas 。2 1+6pas 1+Estop 1+op HUP bf. aUI A ass pass 1 1+Epass 2 A top +op .2 1+8stop f sa sb 0 pb pa pa pb sa Jsb 上游充通大￥
Digital Signal Processing—— IIR Digital Filter Design Bilinear Transformation
Bilinear Transformation Digital Signal Processing--IIR Digital Filter Design ↑i21 ↑jlm[z] π/T 0 Re[z] -π/T s plane s plane z plane 上游充通大￥
Digital Signal Processing—— IIR Digital Filter Design Bilinear Transformation s plane s1 plane z plane