%PART 2
clear
rng(0); %set seed for random number generator for consistent results

N = 256;
T = (0:N-1)/N;
%make trial signal
f=   .5*cos(20 * pi *T) + (1/3)*cos(48*pi*T) + 0.5*randn(1, N); 
forigin = .5*cos(20 * pi *T) + (1/3)*cos(48*pi*T); %signal without noise    

for j=1:N %create central window as vector
    wre(j) = wrect(j-N/2);
end

%have the filter act on f in three steps
yy = fftshift(fft(f)); %centered fft of the signal
zz = fftshift(yy .* wre); %pointwise product shifted back to standard form
xx = real(ifft(zz)); %inverse transform back to time domain yields filtered signal

plot(T, forigin, T, xx) %compare original no-noise signal with filtered one

function y = wrect(x) %function def of rectangular window
if (abs(x) <= 35) 
    y = 1;
else
    y = 0;
end
end