zad2

N  = 32;
n = 0 : 1 : N - 1;
y1 = cos((2 * pi * n / N) + pi / 4);
y2 = 0.5 * cos((4 * pi * n) / N);
y3 = 0.25 * cos((8 * pi * n / N) + pi / 2);
y4 = y1 + y2 + y3;

figure
plot(n, y1, n, y2, n, y3);
xlabel('Numer próbki');
ylabel('Wartość');
legend('y1[n] = cos((2 * pi * n / N) + pi / 4)', 'y2[n] = 0.5 * cos((4 * pi * n) / N)', 'y3[n] = 0.25 * cos((8 * pi * n / N) + pi / 2)');

y1fourier = 2 * fft(y1) / length(y1);
y2fourier = 2 * fft(y2) / length(y2);
y3fourier = 2 * fft(y3) / length(y3);
y4fourier = 2 * fft(y4) / length(y4);

figure
subplot(4,2,1)
stem(abs(y1fourier));

subplot(4,2,2)
stem(abs(y2fourier));

subplot(4,2,3)
stem(abs(y3fourier));

subplot(4,2,4)
stem(abs(y4fourier));


N  = 32 * 8;
n = 0 : 1 : N - 1;
y1 = cos((2 * pi * n / N) + pi / 4);
y2 = 0.5 * cos((4 * pi * n) / N);
y3 = 0.25 * cos((8 * pi * n / N) + pi / 2);
y4 = y1 + y2 + y3;



subplot(4,2,5)
stem(angle(y1fourier));

subplot(4,2,6)
stem(angle(y2fourier));

subplot(4,2,7)
stem(angle(y3fourier));

subplot(4,2,8)
stem(angle(y4fourier));
axis([0 20 -2 2]);