# Documentation

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# cheb2ap

Chebyshev Type II analog lowpass filter prototype

## Syntax

```[z,p,k] = cheb2ap(n,Rs) ```

## Description

`[z,p,k] = cheb2ap(n,Rs)` finds the zeros, poles, and gain of an order `n` Chebyshev Type II analog lowpass filter prototype with stopband ripple `Rs` dB down from the passband peak value. `cheb2ap` returns the zeros and poles in length `n` column vectors `z` and `p` and the gain in scalar `k`. If `n` is odd, `z` is length `n-1`. The transfer function is

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 `cheb1ap`, whose poles are evenly spaced about an ellipse in the left half plane. The Chebyshev Type II stopband edge angular frequency ω0 is set to 1 for a normalized result. This is the frequency at which the stopband begins and the filter has magnitude response of 10–Rs/20.

## Examples

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Design a 6th-order Chebyshev Type II analog lowpass filter with 70 dB of ripple in the stopband. Display its magnitude and phase responses.

```[z,p,k] = cheb2ap(6,70); % Lowpass filter prototype [num,den] = zp2tf(z,p,k); % Convert to transfer function form freqs(num,den) % Frequency response of analog filter```

## Algorithms

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:

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

2. `cheb2ap` subtracts the filter transfer function from unity.

## References

[1] Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.