Elliptic analog lowpass filter prototype
[z,p,k] = ellipap(n,Rp,Rs)
[z,p,k] = ellipap(n,Rp,Rs) returns
the zeros, poles, and gain of an order n elliptic
analog lowpass filter prototype, with Rp dB
of ripple in the passband, and a stopband Rs dB down from the peak value in the passband. The zeros
and poles are returned 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 in factored
zero-pole form is
Elliptic filters offer steeper rolloff characteristics than Butterworth and Chebyshev filters, but they are equiripple in both the passband and the stopband. Of the four classical filter types, elliptic filters usually meet a given set of filter performance specifications with the lowest filter order.
ellipap sets the passband edge angular
frequency ω0 of the elliptic filter to
1 for a normalized result. The passband edge angular frequency is
the frequency at which the passband ends and the filter has a magnitude
response of 10-Rp/20.
ellipap uses the algorithm outlined in [1]. It employs ellipke to
calculate the complete elliptic integral of the first kind and ellipj to calculate Jacobi elliptic functions.
[1] Parks, T. W., and C. S. Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.