Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 41. Chebyshev Filters

Chebyshev filters comprise one of the analog filter families that are commonly used as prototypes for IIR digital filters designed using either the impulse invariance method (Note 50) or the bilinear transformation (Note 51).

Alowpass Chebyshev filter is obtained as an equiripple approximation to the response of an ideal lowpass filter. This approximation yields a filter having a squared magnitude response given by

where

² = 10^r/20 –1

r = passband ripple

    T_n(ω) = Chebyshev polynomial of order n

The first eleven Chebyshev ...