Chebyshev Type-I IIR Filter Design

LIQUID_IIRDES_CHEBY1 is a Chebyshev Type-I filter. This design uses Chebyshev polynomials to create a filter with a sharper transition band than the Butterworth design by allowing ripples in the pass-band. The analog prototype interface is cheby1_azpkf() which computes the \(n\) complex roots \(p_{ak}\) of the \(n^{th}\)-order Chebyshev polynomial.

Attention

talk about analog prototype

An example Chebyshev-I design can be seen in the code listing here:

#include <liquid/liquid.h>
int main()
{
    return 0;
}

An example of a digital filter response can be found in the figure below.

Figure 15 Chebyshev-I filter design, \(n=7\), \(f_c=0.2 F_s\), \(A_p=1\) dB, and \(A_s=60\) dB.

Notice how the performance changes as the order increases to 15…