《DSP using MATLAB》Problem 6.20

先放子函数：

function [C, B, A, rM] = dir2fs_r(h, r);
	% DIRECT-form to Frequency Sampling form conversion
	% ----------------------------------------------------------
	% [C, B, A, rM] = dir2fs_r(h, r)
	%  C = Row vector containing gains for parallel sections
	%  B = matrix containing numerator coefficients arranged in rows
	%  A = matrix containing denominator coefficients arranged in rows
	%  h = impulse response vector of an FIR filter
	% rM = r^M factor needed in the feedforward loop
    %  r = radius of the circle over which samples are taken (r<1)
 
	M = length(h); H = fft(h, M);
	magH = abs(H); phaH = angle(H)';
 
	% check even or odd M
	if (M == 2*floor(M/2))
		L = M/2-1;          % M is even
		%A1 = [1, -1, 0; 1, 1, 0];
		A1 = [1, -r, 0; 1, r, 0];
		C1 = [real(H(1)), real(H(L+2))];
	else
		L = (M-1)/2;        % M is odd
		%A1 = [1, -1, 0];
		A1 = [1, -r, 0];
		C1 = [real(H(1))];
	end
	k = [1:L]';
 
    % initialize B and A arrays
    B = zeros(L, 2); A = ones(L, 3);
    % compute denominator coefficients
    A(1:L, 2) = -2*r*cos(2*pi*k/M);
    A(1:L, 3) = r*r;
    A = [A;A1];
    % compute numerator coefficients
    B(1:L,1) = cos(phaH(2:L+1));
    B(1:L,2) = -r*cos(phaH(2:L+1) - (2*pi*k/M));
    % compute gain coefficients
    C = [2*magH(2:L+1), C1]';
 
    rM = r^M;

　　再放主函数：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 6.20 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%format long;
format short;
fprintf('\n FIR filter DIRECT-form:     \n');
h = [1, 2, 3, 2, 1]/9; 
 
b = h
a = 1.0
 
fprintf('\nConvert DIRECT-form to PARALLEL-form :     \n');
[C, Bp, Ap] = dir2par(b, a)
 
if size(C)==0
  C = 0;
end
 
fprintf('\nConvert DIRECT-form to CASCADE-form :     \n');
[b0, Bc, Ac] = dir2cas(b, a) 
 
fprintf('\nConvert TF-form to SOS-form :     \n');
[sos, g] = tf2sos(b, a)
 
% ----------------------------------------------------------
% NOTE: linear-phase can not use LATTICE-form
% ----------------------------------------------------------
fprintf('\nConvert DIRECT-form to All-Zero LATTICE-form :     \n');
[Klc] = dir2latc(b) 
 
fprintf('\nConvert DIRECT-form to FREQUENCY-SAMPLE-form 1 :     \n');
[Cfs, Bfs, Afs] = dir2fs(b) 
 
fprintf('\nConvert DIRECT-form to FREQUENCY-SAMPLE-form 2 :     \n');
r = 0.9;
[Cfs_r, Bfs_r, Afs_r, rM] = dir2fs_r(b, r) 
 
% -----------------------------------------
%     START check
% -----------------------------------------
n = [0:7];
delta = impseq(0, 0, 7)
%format long
format  short
hcas = casfiltr(b0, Bc, Ac, delta)
 
hltc = latcfilt(Klc, delta)
 
%hladr = ladrfilt(Klr, Clr, delta)
 
hdir = filter(b, a, delta)
% -------------------------------------------
%       END check
% -------------------------------------------

　　运行结果：