Chebyshev Type II analog lowpass filter prototype
[z,p,k] = cheb2ap(n,Rs)
[z,p,k] = cheb2ap(n,Rs) finds
the zeros, poles, and gain of an order
Type II analog lowpass filter prototype with stopband ripple
Rs dB down from the passband peak value.
the zeros and poles in length
n column vectors
the gain in scalar
z is length
n-1. The transfer
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
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.
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
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:
cheb2ap replaces the
frequency variable ω with 1/ω,
turning the lowpass filter into a highpass filter while preserving
the performance at ω = 1.
the filter transfer function from unity.
 Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.