Transform inverse result
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.