er_lpf.m

dsp工具箱

function f = er_lpf(N)
% function f = er_lpf(N)
%   Function to create prototype Butterworth digital LPF using bilinear
%   transformation.  Takes filter order in N (even/odd integer).  Returns transfer function
%   coefficient vectors in struct F.
%
%   Author:  Evan Ruzanski, CU-Boulder, ECEN5632 MATLAB assignment, FA2004

% Filter must be greater than or equal to 2
if (N < 2)
    error('Filter order must be >= 2');
end

% Generate analog prototype Butterworth LPF according to Mitra eq. 5.34
d(1,1:3) = conv([1 -exp(j*pi*(N+1)/(2*N))],[1 -exp(j*pi*(N+3)/(2*N))]);
for k = 2:(N-1)
    d(k,1:k+2) = conv(d(k-1,:),[1 -exp(j*pi*(N+2*(k+1)-1)/(2*N))]);
end
num = [1];
den = real(d(N-1,:)); % Get rid of residual infintesimally small imaginary parts

% Do zero/pole bilinear transformation, T = 2
fs = 1;
k = 1;
z = roots(num);
p = roots(den);
pd = (1+p/fs)./(1-p/fs); % Flip for z^(-1)
zd = (1+z/fs)./(1-z/fs);
kd = (k*prod(fs-z)./prod(fs-p));
zd = [zd;-ones(length(pd)-length(zd),1)];  % Add extra zeros at -1
numd = real(kd*poly(zd));
dend = real(poly(pd));

% Pack parameters into struct
f = struct('tf_complete',{numd,dend});