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Determine the system function H(z) of the lowest order Chebyshev IIR digital filter with the following specifications:

Determine the system function H(z) of the lowest order Chebyshev IIR digital filter with the following specifications: 3 dB ripple in passband 0ω0.2π25 dB attenuation in stopband 0.45πωπ

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Solution:

Let T = 1 and bilinear transformation is used

ε=[1A211]12=[10.70721]=1

The ratio of analog frequencies,

Ω2Ω1=2Ttanω222Ttanω12=tan0.45π2tan0.2π2=2.628

Ncosh1{1ε[1A221]12}cosh1{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 …

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