% Interval endpoints
c = 0;
d = 1;

% Interpolation points
n = 64;
t = c+(d-c)*(0:n-1)/n;

% "Continuous signal"
w = 2*pi/(d-c);
%f = @(t) 1 + cos(2*w*t) + 0.25*sin(10*w*t);
f = @(t) 1 + cos(2*w*t) + 0.25*sin(10*w*t) + 0.2*randn(size(t));


x = f(t);
y = fft(f(t))/sqrt(n);  % Matlab uses different scaling than the textbook

figure(1);
plot(t,x,'b','LineWidth',3);
xlabel('t');  ylabel('x');
figure(2);
%plot(abs(y),'b','LineWidth',3);
plot((1:n)-n/2-1,abs(fftshift(y)),'b','LineWidth',3);
xlabel('k');  ylabel('y');


if 1,
% Low pass filter: cut all waves starting from k_cut
k_cut = 5;
y_filt= zeros(size(y));
% Copy frequencies up to k_cut (remember, in Matlab indexing starts
% from 1)
y_filt(1:k_cut) = y(1:k_cut);
% copy "negative frequencies": the ones from the second half of the
% spectrum
y_filt(n-k_cut+2:n) = y(n-k_cut+2:n);

% recover the filtered signal
x_filt = ifft(y_filt)*sqrt(n);
% plot the original and filtered signals
figure(1);
plot(t,x,'b',...
     t,x_filt,'r');
xlabel('t');  ylabel('x');


end