Organisation of spatial frequencies in FFT2 matrix

Started by Unknown January 6, 2005

Dear all,

My questions relate to the filtering of the 2-d Fourier transform of a square image for a certain range of spatial frequencies, using Matlab.

The image is Fourier analysed using FFT2 and is arranged with the zero-frequency component in the middle of the spectrum using FFTSHIFT.

On the horizontal and vertical axes that pass through the centre of the matrix, is the spatial frequency represented by a specific cell in the matrix linearly related to its distance from the centre of the matrix (in cells)?

Do all instances of a certain, specific spatial frequency fall upon the circumference of a circle that is centred on the zero-frequency component?

If so, why are spatial frequencies are arranged in concentric circular rings when the matrix itself is square?

Thank you very much for your time.