First version of LAB 2

% Problem 2.10(a)

load inputs/lineup.mat

% sound(y, 8192); 

figure;

plot(y)

title('Sound befor filtering');

saveas(gcf, "plots/P2_10_ini_out.png");

close;

% 2.10(a) -------------------------------

x = [1 zeros(1, 1000)];

nx = 0:1000;

he = zeros(1, 1001);

nhe = 0:1000;

for i = 1:1001

    if i < 1001

        he(i) = x(i);

    else

        he(i) = x(i) + 0.5*x(i-1000);

    end    

end

figure;

stem(nhe, he);

title('h_e[n]');

xlabel('n');

saveas(gcf, "plots/P2_10_a_out.png");

close;

% 2.10(b) -------------------------------

% This is not a problem that require to be verified by MATLAB

% 2.10(c) -------------------------------

a = [1 zeros(1, 999) 0.5];

b = [1];

d = [1, zeros(1, 4000)];

nd = 0:4000;

her = filter(b, a, d);

nher = 0:4000;

figure;

stem(nd, her);

title('h_{er}[n]');

xlabel('n');

saveas(gcf, "plots/P2_10_c_out.png");

close;

% 2.10(d) -------------------------------

%  I feel that the given value 1000 and 0.5 are fine. 

a = [1 zeros(1, 999) 0.5]

z = filter(1, a, y);

figure;

plot(z);

title('Sound after filtering');

saveas(gcf, "plots/P2_10_d_out.png");

close;

sound(z, 8192); 

% 2.10(e) -------------------------------

hoa = conv(her, he);

nhoa = (nher(1)+nhe(1)):(nher(end)+nhe(end));

figure;

stem(nhoa, hoa);

title('h_{oa}[n]');

xlabel('n');

saveas(gcf, "plots/P2_10_e_out.png");

close;

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% Problem 2.10(f)

load inputs/lineup.mat

% For y1 ----------------------------------------

ryy1 = conv(y, flip(y));

nryy1 = -(length(y)-1):(length(y)-1);

figure;

plot(nryy1, ryy1);

title('y[n]*y[-n]');

saveas(gcf, "plots/P2_10_f_out1_1.png");

close;

%! Here N is equal to the distance of tow peak.

% N: 1000

% Peak 1: 9967

% Peak 2: 3957

% alpha: 0.4938

N = 1000;

alpha = 0.5;

yo1 = filter([1 zeros(1, N) alpha], 1, y);

sound(yo1, 8192); 

% For y2 ----------------------------------------

ryy2 = conv(y2, flip(y2));

nryy2 = -(length(y2)-1):(length(y2)-1);

figure;

plot(nryy2, ryy2);

title('y_2[n]*y_2[-n]');

saveas(gcf, "plots/P2_10_f_out1_2.png");

close;

% N: 501

% Peak 1: 13160

% Peak 2: 6938

% alpha: 

N = 500;

alpha = 0.5;

yo2 = filter([1 zeros(1, N) alpha], 1, y);

sound(yo2, 8192);

% For y3 ----------------------------------------

ryy3 = conv(y3, flip(y3));

nryy3 = -(length(y3)-1):(length(y3)-1);

figure;

plot(nryy3, ryy3);

title('y_3[n]*y_3[-n]');

saveas(gcf, "plots/P2_10_f_out1_3.png");

close;

% N1: 751

% alpha1: 0.4

% N2: 2252

% alpha2: 0.28

% Peak 1: 14010

% Peak 2: 4884

% Peak 3: 3597

N = 750;

N1 = 2250;

alpha = 0.5;

alpha1 = 0.28;

yo3 = filter([1 zeros(1, N) alpha zeros(1, N1-N-1) alpha1], 1, y);

% sound(yo3, 8192);

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% Problem 2.10(f)

load inputs/lineup.mat

% For y1 ----------------------------------------

ryy1 = conv(y, flip(y));

nryy1 = -(length(y)-1):(length(y)-1);

figure;

plot(nryy1, ryy1);

title('y[n]*y[-n]');

saveas(gcf, "plots/P2_10_f_out1_1.png");

close;

%! Here N is equal to the distance of tow peak.

% N: 1000

% Peak 1: 9967

% Peak 2: 3957

% alpha: 0.4938

N = 1000;

alpha = 0.5;

yo1 = filter(1, [1 zeros(1, N-1) alpha], y);

% sound(yo1, 8192); 

% For y2 ----------------------------------------

ryy2 = conv(y2, flip(y2));

nryy2 = -(length(y2)-1):(length(y2)-1);

figure;

plot(nryy2, ryy2);

title('y_2[n]*y_2[-n]');

saveas(gcf, "plots/P2_10_f_out1_2.png");

close;

% N: 501

% Peak 1: 13160

% Peak 2: 6938

% alpha: 0.1 Too small, the peak is fake !!!!!

N = 500;

alpha = 0.1;

yo2 = filter(1, [1 zeros(1, N-1) alpha], y);

% sound(yo2, 8192);

% For y3 ----------------------------------------

ryy3 = conv(y3, flip(y3));

nryy3 = -(length(y3)-1):(length(y3)-1);

figure;

plot(nryy3, ryy3);

title('y_3[n]*y_3[-n]');

saveas(gcf, "plots/P2_10_f_out1_3.png");

close;

% N1: 751

% alpha1: 0.4

% N2: 2252

% alpha2: 0.28

% Peak 1: 14010

% Peak 2: 4884

% Peak 3: 3597

N = 751;

N1 = 2252;

alpha = 0.5;

alpha1 = 0.28;

b = [1 zeros(1, N-1) alpha zeros(1, N1-1)] + [1 zeros(1, N1-1) alpha1 zeros(1, N-1)];

yo3 = filter(1, b, y);

sound(yo3, 8192);

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