cheb1ap

Chebyshev Type I analog lowpass filter prototype

Description

example

[z,p,k] = cheb1ap(n,Rp) returns the poles and gain of an order n Chebyshev Type I analog lowpass filter prototype with Rp dB of ripple in the passband.

Examples

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Design a 6th-order Chebyshev Type I analog lowpass filter with 3 dB of ripple in the passband. Display its magnitude and phase responses.

[z,p,k] = cheb1ap(6,3);       % Lowpass filter prototype
[num,den] = zp2tf(z,p,k);     % Convert to transfer function form
freqs(num,den)                % Frequency response of analog filter Input Arguments

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Filter order, specified as an integer.

Data Types: single | double

Passband ripple, specified as a scalar in decibels.

Data Types: single | double

Output Arguments

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Zeros of the filter, returned as a matrix.

Poles of the filter, returned as an n-length column vector.

Gain of the filter, returned as a scalar. z is an empty matrix because no zeros exist for this filter design.

Algorithms

Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. The poles are evenly spaced about an ellipse in the left half plane. The Chebyshev Type I passband edge angular frequency ω0 is set to 1.0 for a normalized result. This value is the frequency at which the passband ends. The filter has a magnitude response of 10–Rp/20.

The transfer function is given by

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

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