using Images
using PyPlot
using FFTW

N = 64
x = shepp_logan(N)

figure(1)
clf()
subplot(2,2,1)
imshow(x)

X = fft(x)
subplot(2,2,2)
imshow(abs.(X))

Y = fftshift(X)
subplot(2,2,3)
imshow(abs.(Y))

Y[1:div(N,4)+1,:] .= 0.0
Y[3*div(N,4):end,:] .= 0.0
Y[:,1:div(N,4)+1] .= 0.0
Y[:,3*div(N,4):end] .= 0.0

subplot(2,2,4)
imshow(abs.(Y))


figure(2)
clf()
imshow(abs.(ifft(ifftshift(Y))))



function mydft(x)
  N = length(x)
  y = zeros(ComplexF64,N)

  for l=1:N
    for n=1:N
      y[l] += x[n]*exp(-2*pi*im*(n-1)*(l-1)/N)
    end   
  end
  return y
end