《DSP using MATLAB》Problem 6.22

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 6.22 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%format long;
format short;
 
fprintf('\n FIR filter DIRECT-form:     \n');
h = [1, -4, 6.4, -5.12, 2.048, -0.32768]; 
 
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)
 
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 = 0.99;
[Cfs_r, Bfs_r, Afs_r, rM] = dir2fs_r(b, r) 
 
% ----------------------------------------------------------
% NOTE: linear-phase can not use LATTICE-form
% ----------------------------------------------------------
fprintf('\nConvert DIRECT-form to All-Zero LATTICE-form :     \n');
[Klc] = dir2latc(b) 
 
% -----------------------------------------
%     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
% -------------------------------------------
 
% +++++++++++++++++++++++++++++++++++++++++++++++++
%             5 1st-order section CASCADE-form
% +++++++++++++++++++++++++++++++++++++++++++++++++
broots = roots(b)
L = length(broots)
B1 = ones(L, 2);
 
fprintf('\nConvert DIRECT-form to %d 1st-order section :     \n', L);
for i = 1:1:L
	B1(i,:) = poly( broots(i) );
end
B1
 
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%      CASCADE-form of 1 1st-order section and 2 2nd-order section
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
fprintf('\nConvert DIRECT-form to One 1st-order and Two 2nd-order section:     \n');
B2 = poly( [broots(1), broots(2)] )
B3 = poly( [broots(3), broots(4)] )
B4 = poly( broots(5) )
 
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%      CASCADE-form of 1 2nd-order section and 1 3rd-order section
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
fprintf('\nConvert DIRECT-form to One 2nd-order and One 3rd-order section:     \n');
B5 = poly( [broots(1), broots(2)] )
B6 = poly( [broots(3), broots(4), broots(5)] )

　　运行结果：

直接形式的系数

串联形式系数

频率采样形式系数

格型Lattice形式系数

求出5个零点