《DSP using MATLAB》Problem 6.23

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 6.23 \n\n');

banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%format long;
format short;

broots = [0.5*exp(j*pi/3),  0.5*exp(-j*pi/3),  2*exp(j*pi/3), 2*exp(-j*pi/3), ...
	      0.25*exp(j*pi/6), 0.25*exp(-j*pi/6), 4*exp(j*pi/6), 4*exp(-j*pi/6)]

fprintf('\nConvert DIRECT-form to Cascade of Two Linear-Phase form :     \n');
B1 = real( poly( [broots(1:4)] ) )
B2 = real( poly( [broots(5:8)] ) )

fprintf('\n FIR filter DIRECT-form:     \n');
b = real( poly(broots) )
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
% -------------------------------------------

　　运行结果：

8个零点，即系统函数的分子多项式的根

根据线性相位FIR的特点，前4个零点和后4个零点可分为两组，即看成两个线性相位FIR

串联形式系数

频率采样形式系数