Related to another problem I'm having, I was looking into the workings of
irfft2. These are special versions of the FFT routine, in so far that it needs less input; because you require the real-space image to be real you only need to 'fill' half of Fourier space - due to symmetry, that's all the information you need.
Now, in the docs it is mentioned that performing the inverse transform right after the forward transform should return the original array - to within numerical precision. Time to put this to the test.
If I do the following:
import numpy as np fourier_image = np.random.uniform(-1,1,(100,51)) fourier_recovered = np.fft.rfft2(np.fft.irfft2(fourier_image)) print 'Original power: ', sum(sum(abs(fourier_image)**2.)) print 'Recovered power: ', sum(sum(abs(fourier_recovered)**2.))
... I find the original power and the recovered power differ at the percent level. That seems a rather big difference to me. Am I doing something wrong, or is this just the best we can do?