《DSP using MATLAB》Problem 6.15

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 6.15 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%format long;
format short;
fprintf('\n DIRECT-form:     \n');
b = [1.0  0   -2.20   0  1.6368  0  -0.48928  0  5395456*10^(-8)  0  -147456*10^(-8) ]
a = [1.0  0   -1.65   0  0.8778  0  -0.17281  0  1057221*10^(-8)  0  -893025*10^(-10)]
 
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)
 
fprintf('\nConvert DIRECT-form to LATTICE-LADDER-form :     \n');
[Klr, Clr] = dir2ladr(b, a) 
 
fprintf('\nConvert DIRECT-form to MATLAB LATTICE-LADDER-form :     \n');
[K, V] = tf2latc(b, a)
 
% -----------------------------------------
%     START check
% -----------------------------------------
n = [0:7];
delta = impseq(0, 0, 7)
%format long
format  short
hcas = casfiltr(b0, Bc, Ac, delta)
 
hpar = parfiltr(C, Bp, Ap, delta)
 
hladr = ladrfilt(Klr, Clr, delta)
 
hdir = filter(b, a, delta)
% -------------------------------------------
%       END check
% -------------------------------------------
 
b01 = 1;
Bc1 = [1.0  1.8  0.8;
	   1.0  1.0  0.24;
	   1.0  0.2  0; ];
Ac1 = [1.0  1.6  0.63;
	   1.0  0.8  0.15;
	   1.0  0.1  0;];
fprintf('\nConvert 1st part to DIRECT-form from CASCADE-form :     \n');
[b1, a1] = cas2dir(b01, Bc1, Ac1)
b1 = b1(1:6);
a1 = a1(1:6);
 
fprintf('\nConvert 1st part to PARALLEL-form from DIRECT-form :     \n');
[C1, Bp1, Ap1] = dir2par(b1, a1)
 
if size(C1)==0
  C1 = 0;
end
 
b02 = 1;
Bc2 = [1.0  -1.0  0.24;
	   1.0  -1.8  0.80;
	   1.0  -0.2  0.00; ];
Ac2 = [1.0  -0.8  0.15;
	   1.0  -1.6  0.63;
	   1.0  -0.1  0.00;];
fprintf('\nConvert 2nd part to DIRECT-form from CASCADE-form :     \n');
[b2, a2] = cas2dir(b02, Bc2, Ac2)
b2 = b2(1:6);
a2 = a2(1:6);
 
fprintf('\nConvert 2nd part to PARALLEL-form from DIRECT-form :     \n');
[C2, Bp2, Ap2] = dir2par(b2, a2)
 
if size(C2)==0
  C2 = 0;
end

　　运行结果：

直接形式系数

并联形式系数

串联形式系数

由总的直接形式转换成串联形式，再分成两部分的串联，这两部分写成并联形式，而后串联。

第1部分的并联形式

第2部分的并联形式

题中的附图，系数标注不准的地方直接改了。