%PART 1
clear
rng(0); %set seed for random number generator for conistent results

N = 256;
T = (0:N-1)/N;
%make and plot 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);

plot(T,forigin, T,f)
figure
plot(fftshift(abs(fft(forigin)))); %plot centered spectrum of the pure signal
figure
plot(fftshift(abs(fft(f)))); %plot centered spectrum of the noisy signal
figure

gtent = zeros(1,N); %create the time domain filtered signal
for n = 1:N
    for j=(-N/2 +1):N/2
        gtent(n) = gtent(n) + wtent(j)* f(mymod1(n+j,N));
    end
end

plot(fftshift(abs(fft(gtent)))); %plot centered spectrum of the filtered signal

figure
plot(T,forigin, T, gtent) %compare original no-noisy signal with filtered one

function y = wtent(x)
if (abs(x) <1 ) 
    y = 1/2;
elseif (abs(x) < 2)
    y = 1/4;
else
    y = 0;
end
end

%mymod1 is a utility to reduce indices for circular 
%addition using matlab indexing of 1 to N
function y = mymod1( a,m )
z = mod(a,m);
if z == 0
    y = m;
else
    y = z;
end

end