# cheby2

Chebyshev Type II filter design

## Syntax

## Description

`[`

designs
a lowpass, highpass, bandpass, or bandstop Chebyshev Type II
filter, depending on the value of `b,a`

] = cheby2(`n`

,`Rs`

,`Ws`

,`ftype`

)`ftype`

and the
number of elements of `Ws`

. The resulting bandpass
and bandstop designs are of order 2`n`

.

**Note:** See Limitations for information about numerical issues that affect
forming the transfer function.

`[`

designs
a lowpass, highpass, bandpass, or bandstop digital Chebyshev Type II filter and returns its zeros, poles, and gain. This
syntax can include any of the input arguments in previous syntaxes.`z,p,k`

] = cheby2(___)

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

Chebyshev Type II filters are monotonic in the passband and equiripple in the stopband. Type II filters do not roll off as fast as Type I filters, but are free of passband ripple.

`cheby2`

uses a five-step algorithm:

It finds the lowpass analog prototype poles, zeros, and gain using the function

`cheb2ap`

.It converts poles, zeros, and gain into state-space form.

If required, it uses a state-space transformation to convert the lowpass filter into a bandpass, highpass, or bandstop filter with the desired frequency constraints.

For digital filter design, it uses

`bilinear`

to convert the analog filter into a digital filter through a bilinear transformation with frequency prewarping. Careful frequency adjustment the analog filters and the digital filters to have the same frequency response magnitude at`Ws`

or`w1`

and`w2`

.It converts the state-space filter back to transfer function or zero-pole-gain form, as required.

## Extended Capabilities

## Version History

**Introduced before R2006a**