《DSP using MATLAB》Problem 4.11

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%%            Output Info about this m-file
fprintf(‘\n***********************************************************\n‘);
fprintf(‘        <DSP using MATLAB> Problem 4.11 \n\n‘);

banner();
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format rat;
%% -------------------------------------------------
%%            1      X1(z)    rightsided
%% -------------------------------------------------

b = [1, -1, -4, 4];             nb = [0:3]; 
a = [1, -11/4, 13/8, -1/4];     na = [0:3];                 

%[p, r] = deconv(b, a)
%[p, np, r, nr] = deconv_m(b, nb, a, na)
[R, p, C] = residuez(b, a)

%[delta, n] = impseq(0,0,7);
%x = filter(b, a, delta)

%[b,a] = residuez(R, p, C)

%Mp = abs((p))‘
%Ap = angle((p))‘

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 4.11.1  X1(z)‘)
set(gcf,‘Color‘,‘white‘); 
zplane(b, a);                                           % row vector
title(‘Zero-Pole Plot‘);  xlabel(‘Re‘); ylabel(‘Im‘); grid on;



fprintf(‘\n-------------------- X2(z) ------------------ \n\n‘);
%% -------------------------------------------------
%%            2      X2(z)    absolutely summable
%% -------------------------------------------------

b = [1, 1, -4, 4];              nb = [0:3]; 
a = [1, -11/4, 13/8, -1/4];     na = [0:3];                 

%[p, r] = deconv(b, a)
%[p, np, r, nr] = deconv_m(b, nb, a, na)
[R, p, C] = residuez(b, a)

%[delta, n] = impseq(0,0,7);
%x = filter(b, a, delta)

%[b,a] = residuez(R, p, C)

%Mp = abs((p))‘
%Ap = angle((p))‘

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 4.11.2 X2(z)‘)
set(gcf,‘Color‘,‘white‘); 
zplane(b, a);                                           % row vector
title(‘Zero-Pole Plot‘);  xlabel(‘Re‘); ylabel(‘Im‘); grid on;



fprintf(‘\n-------------------- X3(z) ------------------ \n\n‘);
%% -------------------------------------------------
%%            3      X3(z)    leftsided
%% -------------------------------------------------

b = [1, -3, 4, 1];              nb = [0:3]; 
a = [1, -4, 1, -0.16];          na = [0:3];                 

%[p, r] = deconv(b, a)
%[p, np, r, nr] = deconv_m(b, nb, a, na)
[R, p, C] = residuez(b, a)

%[delta, n] = impseq(0,0,7);
%x = filter(b, a, delta)

%[b,a] = residuez(R, p, C)

Mp = abs((p))‘
Ap = angle((p))‘/pi              % pole angle in pi units

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 4.11.3 X3(z)‘)
set(gcf,‘Color‘,‘white‘); 
zplane(b, a);                                           % row vector
title(‘Zero-Pole Plot‘);  xlabel(‘Re‘); ylabel(‘Im‘); grid on;


fprintf(‘\n-------------------- X4(z) ------------------ \n\n‘);
%% -------------------------------------------------
%%            4      X4(z)    leftsided
%% -------------------------------------------------

b = [0, 0, 1];                  nb = [0:2]; 
a = [1, 2, 1.25, 0.25];         na = [0:3];                 

%[p, r] = deconv(b, a)
%[p, np, r, nr] = deconv_m(b, nb, a, na)
[R, p, C] = residuez(b, a)

%[delta, n] = impseq(0,0,7);
%x = filter(b, a, delta)

%[b,a] = residuez(R, p, C)

%Mp = abs((p))‘
%Ap = angle((p))‘

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 4.11.4 X4(z)‘)
set(gcf,‘Color‘,‘white‘); 
zplane(b, a);                                           % row vector
title(‘Zero-Pole Plot‘);  xlabel(‘Re‘); ylabel(‘Im‘); grid on;


fprintf(‘\n-------------------- X5(z) ------------------ \n\n‘);
%% -------------------------------------------------
%%            5      X5(z)    leftsided
%% -------------------------------------------------

b = [0, 0, 0, 1];                  nb = [0:3]; 
a = [1, 0, -0.5, 0, 0.25*0.25];    na = [0:3];                 

%[p, r] = deconv(b, a)
%[p, np, r, nr] = deconv_m(b, nb, a, na)
[R, p, C] = residuez(b, a)

%[delta, n] = impseq(0,0,7);
%x = filter(b, a, delta)

%[b,a] = residuez(R, p, C)

%Mp = abs((p))‘
%Ap = angle((p))‘

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 4.11.5 X5(z)‘)
set(gcf,‘Color‘,‘white‘); 
zplane(b, a);                                           % row vector
title(‘Zero-Pole Plot‘);  xlabel(‘Re‘); ylabel(‘Im‘); grid on;