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Chebyshev Type II analog lowpass filter prototype

Chebyshev Type II filters are monotonic in the passband and equiripple in the stopband.
The pole locations are the inverse of the pole locations of the `cheb1ap`

function, whose poles are evenly spaced about an ellipse in the left
half plane. The Chebyshev Type II stopband edge angular frequency
*ω*_{0} is set to 1 for a normalized result. This value
is the frequency at which the stopband begins. The filter has a magnitude response of
10^{–Rs/20}.

Chebyshev Type II filters are sometimes called *inverse Chebyshev* filters
because of their relationship to Chebyshev Type I filters. The `cheb2ap`

function is a modification of the Chebyshev Type I prototype algorithm:

`cheb2ap`

replaces the frequency variable*ω*with 1/*ω*, turning the lowpass filter into a highpass filter while preserving the performance at*ω*= 1.`cheb2ap`

subtracts the filter transfer function from unity.

The transfer function is given by

$$H(s)=\frac{z(s)}{p(s)}=k\frac{(s-z(1))(s-z(2))\mathrm{...}(s-z(n))}{(s-p(1))(s-p(2))\mathrm{...}(s-p(n))}.$$

[1] Parks, Thomas W., and C. Sidney Burrus. *Digital Filter
Design*. New York: John Wiley & Sons, 1987.