cheb2ap
Chebyshev Type II analog lowpass filter prototype
Syntax
[z,p,k] = cheb2ap(n,Rs)
Description
[z,p,k] = cheb2ap(n,Rs) finds
the zeros, poles, and gain of an order n Chebyshev
Type II analog lowpass filter prototype with stopband ripple Rs dB down from the passband peak value. cheb2ap returns
the zeros and poles in length n column vectors z and p and
the gain in scalar k. If n is
odd, z is length n-1. The transfer
function is
Chebyshev Type II filters are monotonic in the passband and
equiripple in the stopband. The pole locations are the inverse of
the pole locations of cheb1ap,
whose poles are evenly spaced about an ellipse in the left half plane.
The Chebyshev Type II stopband edge angular frequency ω0 is
set to 1 for a normalized result. This is the frequency at which the
stopband begins and the filter has magnitude response of 10–Rs/20.
Examples
Frequency Response of an Analog Chebyshev Type II Filter
Design a 6th-order Chebyshev Type II analog lowpass filter with 70 dB of ripple in the stopband. Display its magnitude and phase responses.
[z,p,k] = cheb2ap(6,70); % Lowpass filter prototype [num,den] = zp2tf(z,p,k); % Convert to transfer function form freqs(num,den) % Frequency response of analog filter
Algorithms
Chebyshev Type II filters are sometimes called inverse
Chebyshev filters because of their relationship to Chebyshev
Type I filters. The cheb2ap function is a modification
of the Chebyshev Type I prototype algorithm:
cheb2apreplaces the frequency variable ω with 1/ω, turning the lowpass filter into a highpass filter while preserving the performance at ω = 1.cheb2apsubtracts the filter transfer function from unity.
References
[1] Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.