Jump to content

Talk:Fractional Fourier transform

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Jhealy (talk | contribs) at 18:57, 14 August 2009. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

fractional fourier transfrom - a significant revolution??

Yes, it is. Namias introduced it to quantum mechanics, but I'm not sure what they use it for in that field. In optics though, it's quite important. The relevant paper is, A.W. Lohmann, “Image rotation, Wigner rotation and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). That introduced it to the optics community, which uses it to model the effect of quadratic phase systems. - jhealy 22:13, Aug 24, 2006 (GMT)

How does one actually understand the Figure "Time/Frequency Distribution of Fractional Fourier Transform."? I find this quite confusing, are these actually spectrograms? —Preceding unsigned comment added by Dai mingjie (talkcontribs) 19:55, 27 July 2009 (UTC)[reply]

I believe they are spectrograms, or at least something similar, like a Cohen class distribution. The behaviour is consistent with what I'd expect of those, though it's all clean enough that it may be illustrative rather than really generated from data. If you have a signal processing background, you might be confused by the origin being at the centre - a convention from Fourier optics.
The first image is a sinusoid, and the last one is a pair of delta functions, the Fourier transform of the first. The others are intermediate rotations, and would appear to be chirps if viewed as a time- or space-varying signal. Jhealy (talk) 18:57, 14 August 2009 (UTC)[reply]