Transform inverse result let us assume that:
 f is a grayscale image of size NxN, and F is the Fourier transform of f.

G is a 2Nx2N transform obtained by inserting 0 between every value in F:


What is the inverse transform of G?

solution:
so i have programmed it, and the picture will be 4 times bigger with the picture 4 times in it. g= [f f;f f]
can you please explain why this is the answer?
Think of it the other way around. 
If you duplicate an image then you get zeros in between the transform (
This can intuitively be explained: 
duplicating an image is like convolving with 2 deltas (comb) of wavelength 1/2 the new image size. so is equivalent under convolution theorem to multiplying with comb of freq size of image / 2 which gives a comb with delta every other pixel -> every other pixel is zero.