a) In MATLAB read an image and apply 2D FFT routine in MATLAB. Display the Fourier spectrum image.

b) Now take the 2D inverse Fourier transform of the spectrum image to recover the spatial domain image.

c) Subtract this image from the original image. Does the image contain all zero values?

Here's some MATLAB base code to get you started:

clc; clear all;

% Image reading

img = imread('pens1.jpg');

img = rgb2gray(img);

% Show original image

imshow(img);

% 2d fft

imgfft2 = fft2(img);

% 2d inverse fft

b = ifft2(imgfft2);

% Show image's 2d spectrum

figure;

a = uint8(abs(imgfft2));imshow(a);

% Show reconstructed image

figure; imshow(uint8(b));