update

% Problem 2.10(f)

load inputs/lineup.mat

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

B = [1];

z = filter(B, A, y);

z=z';

rxx=conv(z, fliplr(z));

% 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");

a1=rxx(7000);b1=2*rxx(8000);c1=rxx(7000)-ryy1(7000);

d1=b1^2-4*a1*c1;

x1=(-b1+d1^0.5)/(2*a1);

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

% N:1000

% Peak 1: 9976

% Peak 2: 3957

% alpha: 0.5

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");

a2=rxx(7000);b2=2*rxx(7501);c2=rxx(7000)-ryy2(7000);

d2=b2^2-4*a2*c2;

x2=(-b2+d2^0.5)/(2*a2);

% N: 501

% Peak 1: 13160

% Peak 2: 6938

% alpha: 0.7

N = 500;

alpha = 0.7;

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");

% N1: 751

% alpha1: 0.75

% N2: 2252

% alpha2: 0.6

% Peak 1: 14010

% Peak 2: 4884

% Peak 3: 3597

N = 751;

N1 = 2252;

alpha1 = 0.75;

alpha2 = 0.6;

b = [1 zeros(1, N-1) alpha1 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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A = [1 zeros(1, 999) 0.5];

B = [1];

z = filter(B, A, y);

z=z';

rxx=conv(z, fliplr(z));

stem(rxx);

% 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");

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

a1=rxx(7000);b1=2*rxx(8000);c1=rxx(7000)-ryy1(7000);

d1=b1^2-4*a1*c1;

x1=(-b1+d1^0.5)/(2*a1);

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

% N:1000

% Peak 1: 9976

% Peak 2: 3957

% alpha: 0.5

N = 1000;

alpha = 0.5;

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

% sound(yo1, 8192); 

yo1 = filter(1, [1 zeros(1, N-1) x1], y);

sound(yo1, 8192); 

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

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

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

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

a2=rxx(7000);b2=2*rxx(7501);c2=rxx(7000)-ryy2(7000);

d2=b2^2-4*a2*c2;

x2=(-b2+d2^0.5)/(2*a2);

% N: 501

% Peak 1: 13160

% Peak 2: 6938

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

% alpha: 0.7

N = 500;

alpha = 0.1;

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

% sound(yo2, 8192);

N = 501;

yo2 = filter(1, [1 zeros(1, N-1) x2], y2);

sound(yo2, 8192);

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

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

% N1: 751

% alpha1: 0.4

% alpha1: 0.75

% N2: 2252

% alpha2: 0.28

% alpha2: 0.6

% Peak 1: 14010

% Peak 2: 4884

% Peak 3: 3597

N = 751;

N1 = 2252;

alpha = 0.4;

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);

alpha1 = 0.75;

alpha2 = 0.6;

b = [1 zeros(1, 750) alpha1 zeros(1, 1500) alpha2] ;

yo3 = filter(1, b, y3);

sound(yo3, 8192);

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