Posted by
Joachim Wesner on
Apr 23, 2010; 9:05am
URL: http://imagej.273.s1.nabble.com/FFT-averaging-tp3688496p3688507.html
Hi there
>I guess I have to dust off my Oppenhein and Schafer. Still I have to
>wonder why periodograms are averaged in the frequency domain if the time
>domain would work as well.
If you imagine the SAME 1 or 2D distribution (image) invariant over time
(within a stack), with only
variable noise, averaging the input distribution or averaging the final
*complex* FFT spectrum
will give the same result.
If the input distribution changes over time / within the stack, clearly in
the limit of many images
the average of the input will vanish (cancel out) as will the average of
the individual complex transforms.
This will likely happen even if the individual "frequency contents" within
the images are similar,
because the phase relations in the general case will not be "congruent"
with the "sampling interval"
between the images.
However,if you only want to know the "power spectrum" of a time variant
distribution, you can average
over the individual power spectra which are not "phase sensitive". I think
this is what you refer to in
"averaging of peridograms in the frequency domain"
Mit freundlichen Grüßen / Best regards
Joachim Wesner
Leica Microsystems CMS GmbH | GmbH mit Sitz in Wetzlar | Amtsgericht
Wetzlar HRB 2432
Geschäftsführer: Dr. Stefan Traeger | Dr. David Roy Martyr | Colin Davis
www.leica-microsystems.com
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