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Chebyshev Type I filter design

`[b,a] = cheby1(n,Rp,Wp)`

`[b,a] = cheby1(n,Rp,Wp,ftype)`

`[z,p,k] = cheby1(___)`

`[A,B,C,D] = cheby1(___)`

`[___] = cheby1(___,'s')`

`[`

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

] = cheby1(`n`

,`Rp`

,`Wp`

,`ftype`

)`ftype`

and the
number of elements of `Wp`

. 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 I filter and returns its zeros, poles, and gain. This
syntax can include any of the input arguments in previous syntaxes.`z,p,k`

] = cheby1(___)

Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. Type I filters roll off faster than Type II filters, but at the expense of greater deviation from unity in the passband.

`cheby1`

uses a five-step algorithm:

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

`cheb1ap`

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

If required, it uses a state-space transformation to convert the lowpass filter to a highpass, bandpass, 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 enables the analog filters and the digital filters to have the same frequency response magnitude at`Wp`

or`w1`

and`w2`

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