《DSP using MATLAB》Problem 4.23

代码：

%% ------------------------------------------------------------------------

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 4.23 \n\n');

banner();

%% ------------------------------------------------------------------------

% ----------------------------------------------------

%               1        H1(z)

% ----------------------------------------------------

b = [1, -0.866, -1.2278, 0.7938];  nb = [-1:2];

a = [1, -0.7, -0.81, 0.567]*0.7;   na = [0:3];            %

[p, np, r, nr] = deconv_m(b, nb, a, na)

b1 = [-0.1660, -0.4178, 0.2268]

[R, p, C] = residuez(b1, a)

Mp = (abs(p))'

Ap = (angle(p))'/pi

%% ------------------------------------------------------

%%   START a    determine Y(z) and sketch

%% ------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'P4.23 Y(z) its pole-zero plot')

set(gcf,'Color','white');

zplane(b,a);

title('pole-zero plot'); grid on;

%% ----------------------------------------------

%%    END

%% ----------------------------------------------

% ------------------------------------

%                  h(n)

% ------------------------------------

[delta, n] = impseq(0, 0, 19);

h_check = filter(b, a, delta)                                             % check sequence

[delta1, n1] = sigshift(delta, n, -1);

h_answer1 = 1.4286*delta1;

h_answer2 = 0.2323*(-0.9).^n.*stepseq(0,0,19) - 1.1257*(0.9).^n.*stepseq(0,0,19) + 0.6563*(0.7).^n.*stepseq(0,0,19);         % answer sequence

[h_answer, n2] = sigadd(h_answer1, n1, h_answer2, n)

　　运行结果：

Y(z)进行部分分式展开，

其留数及对应极点为：

零极点图如下

输出y(n)的前20个元素（这里变量名称h_check、h_answer用的不合适。）