buttap.m

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function [z,p,k] = buttap(n)
%BUTTAP Butterworth analog lowpass filter prototype.
%   [Z,P,K] = BUTTAP(N) returns the zeros, poles, and gain
%   for an N-th order normalized prototype Butterworth analog
%   lowpass filter.  The resulting filter has N poles around
%   the unit circle in the left half plane, and no zeros.
%
%   See also BUTTER, CHEB1AP, CHEB2AP, ELLIPAP.

%   Author(s): J.N. Little and J.O. Smith, 1-14-87
%   	   L. Shure, 1-13-88, revised
%   Copyright (c) 1988-98 by The MathWorks, Inc.
%   $Revision: 1.11 $  $Date: 1997/11/26 20:13:06 $

% Poles are on the unit circle in the left-half plane.
z = [];
p = exp(i*(pi*(1:2:n-1)/(2*n) + pi/2));
p = [p; conj(p)];
p = p(:);
if rem(n,2)==1   % n is odd
    p = [p; -1];
end
k = real(prod(-p));