FFT multiplication

Posted by Winnok H. De Vos on Dec 25, 2008; 11:25am
URL: http://imagej.273.s1.nabble.com/FFT-filter-conversion-to-real-space-tp3694163p3694165.html

Dear All,

I would like to take the opportunity to ask another question regarding  
Fourier operations. I would like to perform spatiotemporal image  
correlation in the Fourier domain because of speed and memory  
considerations.
If I understand correctly, convolution of two images (i.e.  
correlation) in the spatial domain, equals mere multiplication of the  
Fourier transformed images in the frequency domain.
However, when multiplying two FFT images, the resulting images is no  
longer expressed in polar coordinates and therefore cannot be  
transformed back by inverse FFT. I tried FD Math correlate, but this  
operation requires two square images of fixed dimensions and I'm not  
sure if enlarging the canvas size goes without consequences for the  
correlation outcome. I have noticed that the latter operation appears  
to give a similar resulting image whether one uses the original images  
as input or the Fourier transformed.
Could anybody please share on how to do this the right way?
Many thanks in advance and best wishes,

Winnok

ps: the archives were unaccesible, so apologies if this is a duplicate query.