cheb1ap

Chebyshev Type I analog lowpass filter prototype

Syntax

[z,p,k] = cheb1ap(n,Rp)

Description

[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

Frequency Response of an Analog Chebyshev Type I Filter

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

n — Filter order

integer

Filter order, specified as an integer.

Data Types: single | double

Rp — Passband ripple

scalar

Passband ripple, specified as a scalar in decibels.

Data Types: single | double

Output Arguments

z — Zeros

matrix

Zeros of the filter, returned as a matrix.

p — Poles

n-length column vector

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

k — Gain

scalar

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

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

References

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

All inputs must be constants. Expressions or variables are allowed if their values do not change.