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%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 4.15 \n\n');

banner();

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%%            1      h(n)=[5(0.25)^n]u(n)

%%                   x(n)=(0.25^n)u(n)

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

n = [0:9];

h1 = 5 * (1/4) .^ n .* stepseq(0, 0, 9);

x  = (1/4) .^ n;

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 h1(n) x(n)')

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

subplot(2,1,1); stem(n, h1);

xlabel('n'); ylabel('h(n)'); grid on;

title('h(n)=[5(1/4)^n]u(n)');

subplot(2,1,2); stem(n, x);

xlabel('n'); ylabel('x'); grid on;

title('x(n)=(1/4)^nu(n)');

b1 = [5]; a1 = [1, -1/4];                  

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 H1(z) pole-zero')

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

zplane(b1, a1);

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

y1 = filter(b1, a1, x);

[y1_chk, ny1_chk] = conv_m(h1, n, x, n);

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 y1(n)')

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

subplot(2,1,1); stem([0:length(y1)-1], y1);

xlabel('n'); ylabel('h(n)'); grid on;

title('y(n)=filter(b, a, x)');

subplot(2,1,2); stem(ny1_chk, y1_chk);

xlabel('n'); ylabel('y'); grid on;

title('y(n)=h(n)*x(n)');

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%%            2      h(n)=[n(1/3)^n+(-1/4)^n]u(n)

%%                   x(n)=(0.25^n)u(n)

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

n = [0:9];

h2 = (n .* (1/3) .^ n + (-1/4) .^ n ) .* stepseq(0, 0, 9);

x  = (1/4) .^ n;

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 h2(n) x(n)')

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

subplot(2,1,1); stem(n, h2);

xlabel('n'); ylabel('h(n)'); grid on;

title('h(n)=[n(1/3)^n]u(n) + (-1/4)^nu(n)');

subplot(2,1,2); stem(n, x);

xlabel('n'); ylabel('x'); grid on;

title('x(n)=(1/4)^nu(n)');

%b2 = [0, 12, 48, -1]; a2 = [144, -24, -23, 2, 1];

b2 = [1, -1/3, 7/36]; a2 = [1, -5/12, -1/18, 1/36];

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 H2(z) pole-zero')

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

zplane(b2, a2);

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

y2 = filter(b2, a2, x);

[y2_chk, ny2_chk] = conv_m(h2, n, x, n);

figure('NumberTitle', 'off', 'Name', 'Problem 4.15 y2(n)')

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

subplot(2,1,1); stem([0:length(y2)-1], y2); axis([0, 9, 0, 1]);

xlabel('n'); ylabel('h(n)'); grid on;

title('y(n)=filter(b, a, x)');

subplot(2,1,2); stem(ny2_chk, y2_chk); axis([0, 9, 0, 1]);

xlabel('n'); ylabel('y'); grid on;

title('y(n)=h(n)*x(n)');