# cheb2ap

Chebyshev Type II analog lowpass filter prototype

## Syntax

## Description

## Examples

## Input Arguments

## Output Arguments

## Algorithms

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

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

## References

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

## Extended Capabilities

## Version History

**Introduced before R2006a**