# Why is the size of results from FFT half the size of the input, while that is not the case in image processing?

When dealing with real data, Fourier Transform produces symmetric results and FFT algorithms discards half of it. An input with 1024 points will yield only 513 points in the output.

However, in image processing, when Fourier Transform is calculated, the size of the output image is same as that of the input image. Assume that the images are 2D. The (pixel) value of image function f(x, y) is still real. So, why do we still have an output image size same as input?

• An FFT with 1024 real valued inputs produces 1024 scalar valued outputs, 2 outputs as real values, and 1022 outputs values as pairwise components of 511 complex points. – hotpaw2 Feb 1 at 21:23