Creating a grid in Fourier-space

1. May 2, 2012

Mizuti

Hello,

I'm new here and not sure where to put this question, which is more of a mathematical question, but also involves some programming in python (mainly the use of numpy.fft).

I have a code which creates a square image with dimensions 4x4 arcsec running from -2 arcsec to +2 arcsec and is created on an 80x80 grid. To this I want to add another image. This second image is created through a FFT of an 80x80 grid and thus starts out in Fourier space. After the FFT, I want the image to have exactly the same dimensions in real space as the first image.

Because Fourier space represents the scales and the wavenumber is defined as k = 2pi/x (although in this case the numpy.fft uses the definition where I think k = 1/x), I thought the largest scale would have to have the smallest k-value and the smallest scale the largest k-value.

So if x_max = 2 (the dimensions in the x-direction of the first image) and dim_x = 80 (the number of columns in the grid):

k_x,max = 1/(2*x_max/dim_x)

k_x,min = 1/(2*x_max)

and let the grid in Fourier-space run from k_x,min to k_x,max (same for the y-direction)

I hope I explained this clearly enough, but I haven't been able to find any confirmation or explanation for this in the literature about FFT's and would really like to know if this correct.