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function [z,p,k] = cheb1ap(n, rp) %CHEB1AP Chebyshev type I analog lowpass filter prototype. % [Z,P,K] = CHEB1AP(N,Rp) returns the zeros, poles, and gain % of an N-th order normalized prototype type I Chebyshev analog % lowpass filter with Rp decibels of ripple in the passband. % Type I Chebyshev filters are maximally flat in the stopband. % % See also CHEBY1, CHEB1ORD, BUTTAP, CHEB2AP, ELLIPAP. % Author(s): L. Shure, 1-13-88 % Copyright (c) 1988-98 by The MathWorks, Inc. % $Revision: 1.1 $ $Date: 1998/06/03 14:42:13 $ epsilon = sqrt(10^(.1*rp)-1); mu = asinh(1/epsilon)/n; p = exp(j*(pi*(1:2:2*n-1)/(2*n) + pi/2)).'; p = sinh(mu)*real(p) + j*cosh(mu)*imag(p); z = []; k = real(prod(-p)); if ~rem(n,2) % n is even so patch k k = k/sqrt((1 + epsilon^2)); end