Chebyshev Type I analog lowpass filter prototype
[z,p,k] = cheb1ap(n,Rp)
[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. The function returns the poles in the length n column vector p and the gain in scalar k. z is an empty matrix, because there are no zeros. The transfer function is
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 is the frequency at which the passband ends and the filter has magnitude response of 10–Rp/20.
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
 Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.