cheby1
Chebyshev Type I filter design
Syntax
Description
[
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 2n
.
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(___)
Examples
Input Arguments
Output Arguments
More About
Algorithms
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 atWp
orw1
andw2
.It converts the state-space filter back to transfer function or zero-pole-gain form, as required.
Extended Capabilities
Version History
Introduced before R2006a