clear;

% exercice 1

f1 = 1000;
f2 = 3000;
N = 100;

Fe = 10000;
Te = 1/Fe;

T = [0:Te:(N-1)*Te];

Y1 = cos(2*pi*f1 * T);
Y2 = cos(2*pi*f2 * T);

Ys = Y1 + Y2;
% plot(T, Ys);
% hold;

% fft discrète
% semilogy([0:N-1]/N*Fe, abs(fft(Ys, N)));



% exercice 2

fc_tild = 1000/Fe;
A = 1;

ordre = 10;
B = 2*fc_tild * sinc(2*fc_tild * [-ordre/2:1:ordre/2]);
%plot(B);
%hold;

ordre = 60;
B = 2*fc_tild * sinc(2*fc_tild * [-ordre/2:1:ordre/2]);
%plot(B);



% exercice 3

fc_tild = 1000/Fe;
A = 1;

ordre = 10;
B = 2*fc_tild*sinc(2*fc_tild * [-ordre/2:1:ordre/2]);
Yf = filter( B, A, Ys);
semilogy([0:N-1]/N*Fe, abs(fft(Yf, N)));

hold;

ordre = 60;
B = 2*fc_tild*sinc(2*fc_tild * [-ordre/2:1:ordre/2]);
Yf = filter( B, A, Ys);
semilogy([0:N-1]/N*Fe, abs(fft(Ys, N)));



legend;