《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