update lab 2

% Problem 2.5(d)

a = [1 -3/5];

b = 1;

x = [1 zeros(1,19)];

h1 = filter(b, a, x);

h2 = zeros(1,21);

nh = 0:19;

for i = 2:21

    h2(i) = ((3/5)^(i-2)) * h2(i-1) + x(i-1)

end

h2 = h2(2:end);

subplot(2, 1, 1);

stem(nh, h1);

title('y_1[n]=(3/5)y_1[n-1]+x[n]');

xlabel('n');

ylabel('h_1[n]');

subplot(2, 1, 2);

stem(nh, h2);

title('y_2[n]=(3/5)^ny_1[n-1]+x[n]');

xlabel('n');

ylabel('h_2[n]');

saveas(gcf, "plots/P2_5_d_out.png");

close;

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% Problem 2.5(e)

a = [1 -3/5];

b = 1;

x = ones(1, 20);

s1 = filter(b, a, x);

s2 = zeros(1,21);

ns = 0:19;

for i = 2:21

    s2(i) = ((3/5)^(i-2)) * s2(i-1) + x(i-1)

end

s2 = s2(2:end);

subplot(2, 1, 1);

stem(ns, s1);

title('y_1[n]=(3/5)y_1[n-1]+x[n]');

xlabel('n');

ylabel('s_1[n]');

subplot(2, 1, 2);

stem(ns, s2);

title('y_2[n]=(3/5)^ny_1[n-1]+x[n]');

xlabel('n');

ylabel('s_2[n]');

saveas(gcf, "plots/P2_5_e_out.png");

close;

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% Problem 2.5(f)

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% Problem 2.5(g)

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