a) Generate a 64 × 64 image with a square object f ( x, y ) = 50, 28 = x, y = 35 ; f ( x, y ) = 0, otherwise

b) Calculate and display the magnitude and phase of the 2D Fourier Transform of f ( x, y )

c) Multiply by (-1)^(x+y) , recalculate and display the magnitude of the 2D Fourier Transform.

d) Discuss your results with regard to symmetry properties of Fourier Transform.

e) Verify the separability property of 2-dimensional Fourier Transform using the example in (a) above (i.e., use Matlab, 2D FFT and appropriate sequence of 1D FFTs). Display the magnitude of the spectrum as i. F (u, v)

ii. D(u, v) = log(1 + F (u , v) )

f) Verify the rotation property of the two dimensional Fourier Transforms using the image in (a).