written 2.3 years ago by | • modified 2.3 years ago |
Determine the system function H(z) of the lowest order Chebyshev IIR digital filter with the following specifications: 3 dB ripple in passband 0≤ω≤0.2π25 dB attenuation in stopband 0.45π≤ω≤π
written 2.3 years ago by | • modified 2.3 years ago |
Determine the system function H(z) of the lowest order Chebyshev IIR digital filter with the following specifications: 3 dB ripple in passband 0≤ω≤0.2π25 dB attenuation in stopband 0.45π≤ω≤π
written 2.3 years ago by |
Solution:
Let T = 1 and bilinear transformation is used
ε=[1A21−1]12=[10.7072−1]=1
The ratio of analog frequencies,
Ω2Ω1=2Ttanω222Ttanω12=tan0.45π2tan0.2π2=2.628
N≥cosh−1{1ε[1A22−1]−12}cosh−1{Ω2Ω1}
$ \begin{aligned} & \geq \frac{\cosh ^{-1}\left\{\frac{1}{1}\left[\frac{1}{0.0562^2}-1\right]^{\frac{1}{2}}\right\}}{\cosh ^{-1}(2.628]} \\ & \geq \frac{3.569}{1.621} \geq 2.20 \approx …