close all
clear all 
clc

load('homework2.mat') % defines t, x, T
x = x - mean(x);
x = [x, zeros(1,2*length(x))]; % trick to tighthen Fourier sampling
N = length(x);
t = (0:N-1)*T;
X = fftshift(T*fft(x));
om = (-round((N-1)/2):round(N/2)-1) *2*pi/(N*T); 
Y = X.*(abs(om)>pi); % filter signal
y = ifft(ifftshift(Y)/T); % filtered signal in time

figure(1)
subplot(2,2,1)
plot(t,x)
grid
xlabel('t')
ylabel('x(t)')
title('time domain - distorted')
axis([0 20 ylim])
subplot(2,2,2)
plot(t,y)
grid
xlabel('t')
ylabel('y(t)')
title('time domain - filtered')
axis([0 20 ylim])
subplot(2,2,3)
semilogy(om,abs(X))
axis([xlim 5e-2 5e3])
grid
xlabel('\omega')
ylabel('X(\omega)')
axis([0 20 1e1 1e4])
title('Fourier domain - distorted')
subplot(2,2,4)
semilogy(om,abs(Y))
grid
xlabel('\omega')
ylabel('Y(\omega)')
axis([0 20 1e1 1e4])
title('Fourier domain - filtered')

% printing figure in png format
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 4.5])
print -dpng homework2.png -r100