cheb2ap - Chebyshev Type II analog lowpass filter prototype

Syntax

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.

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:

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.

References

[1] Parks, T.W., and C.S. Burrus. Digital Filter Design, New York: John Wiley & Sons, 1987. Chapter 7.

See Also

besselap | buttap | cheb1ap | cheby2 | ellipap

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