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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 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.


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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

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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:

  1. cheb2ap replaces the frequency variable ω with 1/ω, turning the lowpass filter into a highpass filter while preserving the performance at ω = 1.

  2. cheb2ap subtracts the filter transfer function from unity.


[1] Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.

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