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Characteristics of Prototype Analog Filters 421
function [b,a] = u_elipap(N,Rp,As,Omegac);
% Unnormalized Elliptic Analog Lowpass Filter Prototype
% -----------------------------------------------------
% [b,a] = u_elipap(N,Rp,As,Omegac);
% b = numerator polynomial coefficients
% a = denominator polynomial coefficients
% N = Order of the Elliptic Filter
% Rp = Passband Ripple in dB; Rp > 0
% As = Stopband Attenuation in dB; As > 0
% Omegac = Cutoff frequency in radians/sec
%
[z,p,k] = ellipap(N,Rp,As);
a = real(poly(p)); aNn = a(N+1);
p = p*Omegac; a = real(poly(p)); aNu = a(N+1);
b = real(poly(z)); M = length(b); bNn = b(M);
z = z*Omegac; b = real(poly(z)); bNu = b(M);
k = k*(aNu*bNn)/(aNn*bNu);
b0 = k; b = k*b;
Using the U elipap function, we provide a function called afd elip
to design an analog elliptic lowpass filter, given its specifications. This
follows and uses the filter order computation formula given in (8.62).
function [b,a] = afd_elip(Wp,Ws,Rp,As);
% Analog Lowpass Filter Design: Elliptic
% --------------------------------------
% [b,a] = afd_elip(Wp,Ws,Rp,As);
% b = Numerator coefficients of Ha(s)
% a = Denominator coefficients of Ha(s)
% Wp = Passband edge frequency in rad/sec; Wp > 0
% Ws = Stopband edge frequency in rad/sec; Ws > Wp > 0
% Rp = Passband ripple in +dB; (Rp > 0)
% As = Stopband attenuation in +dB; (As > 0)
%
if Wp