Filters.m

clf;
close all;

%
%5.2.1
%
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N = size(X,1);
xplot = linspace(1,N,N);

figure('name','1-4')
%subplot(1,2,1);
%plot(xplot,X);

omega = pi/30;
A = tan(omega/2);
X = [X(1); X(1); X];
Y = [0; 0];
for i = 3:N + 2
    Y(i) = (  A^2 * (X(i) + 2*X(i - 1) + X(i - 2)) + 2*(1 - A^2)*Y(i - 1) - (1 - sqrt(2)*A + A^2)*Y(i - 2)  )/(1 + sqrt(2)*A + A^2);
end
Y(1) = [];
Y(2) = [];

subplot(2,2,1);
plot(xplot,Y);
title('5.2.1');



%
%5.2.2
%

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N = size(X,1);
xplot = linspace(1,N,N);

%figure('name','5.2.2')
%subplot(1,2,1);
%plot(xplot,X);

omega = 19*pi/20;
C = cot(omega/2);
X = [X(1); X(1); X];
Y = [0; 0];
for i = 3:N + 2
    Y(i) = (  C^2 * (X(i) - 2*X(i - 1) + X(i - 2)) + 2*(C^2 - 1)*Y(i - 1) - (1 - sqrt(2)*C + C^2)*Y(i - 2)  )/(1 + sqrt(2)*C + C^2);
end
Y(1) = [];
Y(2) = [];

subplot(2,2,2);
plot(xplot,Y);
title('5.2.2');
%
%5.2.3
%

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N = size(X,1);
xplot = linspace(1,N,N);

%figure('name','5.2.3')
%subplot(1,2,1);
%plot(xplot,X);

omega = 5*pi/6;
B = pi/20;
D = cos(omega)/cos(B);
E = tan(B);
X = [X(1); X(1); X];
Y = [0; 0];
for i = 3:N + 2
    Y(i) = (    E*X(i) - E*X(i - 2) + 2*D*Y(i - 1) - (1 - E)*Y(i - 2)    )/(E + 1);
end
Y(1) = [];
Y(2) = [];

subplot(2,2,3);
plot(xplot,Y);
title('5.2.3');


%
%5.2.4
%

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859.0966679768378];

N = size(X,1);
xplot = linspace(1,N,N);

% figure('name','5.2.4')
% subplot(1,2,1);
% plot(xplot,X);

omega = pi/3;
B = pi/10;
D = cos(omega)/cos(B);
E = tan(B);
Y = [0; 0];
for i = 3:N
    Y(i) = (    X(i) - 2*D*X(i - 1) + X(i - 2) + 2*D*Y(i - 1) - (1 - E)*Y(i - 2)    )/(E + 1);
end
Y(1) = [];
Y(2) = [];

newplot = linspace(1,N - 2,N - 2);
subplot(2,2,4);
plot(newplot(20:N - 2),Y(20:N - 2));  %20 unstable points at the beginning removed
title('5.2.4');

%
%5.2.8
%

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%first filter (pi/8)
N = size(X,1);
xplot = linspace(1,N,N);

figure('name','5.2.8')
subplot(2,2,1);
plot(xplot,X);
title('Data');

omegamin = pi/8;
B = pi/15;
D = cos(omegamin);
E = tan(B);
Y = [0; 0];
for i = 3:N
    Y(i) = (    X(i) - 2*D*X(i - 1) + X(i - 2) + 2*D*Y(i - 1) - (1 - E)*Y(i - 2)    )/(E + 1);
end
Y(1) = [];
Y(2) = [];

newplot = linspace(1,N - 2,N - 2);
subplot(2,2,2);
plot(newplot,Y);
title('pi/8 band-reject');

%second filter (pi/7)
X = Y;
N = size(X,1);

omegamin = pi/7;
B = pi/15;
D = cos(omegamin);
E = tan(B);
Y = [0; 0];
for i = 3:N
    Y(i) = (    X(i) - 2*D*X(i - 1) + X(i - 2) + 2*D*Y(i - 1) - (1 - E)*Y(i - 2)    )/(E + 1);
end
Y(1) = [];
Y(2) = [];

cut = 20; %remove 20 unstable points from the beginning
Y(1:cut) = [];
newplot = linspace(1,N - 2 - cut,N - 2 - cut);
subplot(2,2,3);
plot(newplot,Y);
title('pi/8 and pi/7 band-rejects');

%third filter (low-pass pi/10)
X = Y;
N = size(X,1);

omega = pi/10;
A = tan(omega/2);
X = [X(1); X(1); X];
Y = [0; 0];
for i = 3:N + 2
    Y(i) = (  A^2 * (X(i) + 2*X(i - 1) + X(i - 2)) + 2*(1 - A^2)*Y(i - 1) - (1 - sqrt(2)*A + A^2)*Y(i - 2)  )/(1 + sqrt(2)*A + A^2);
end
Y(1) = [];
Y(2) = [];

xplot = linspace(1,N,N);
subplot(2,2,4);
plot(xplot,Y);
title('band-rejects + low-pass');