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
analog lowpass filter prototype, with
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
the gain in scalar
z is length
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.
 Parks, T. W., and C. S. Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.