Talk:Fractional Fourier transform

message: It would be nice to have a plot of what the basis functions look like, that the FrFT is analysing the signal into linear combinations of.
If one takes a spike, and applies an inverse-FrFT to it, what does the result look like plotted as a time-domain signal?  Jheald (talk) 12:21, 12 July 2011 (UTC)
thread_title:  Basis functions 

message: Could you elaborate on the meaning of bosonic and fermionic in the context
of harmonic decompositions? The links of the adjectives go to rather general
articles about the particles in physics.  — Preceding unsigned comment added by 2001:4CA0:4E01:0:221:28FF:FE3C:B197 (talk) 09:22, 4 April 2013 (UTC)
thread_title:  Elaborate on the meaning of bosonic and fermionic in this context 

message: (1) Is there an issue "Properties->integer order"? I think the sentence "When alpha is equal to an integer k, the alpha-th order fractional Fourier transform is equivalent to the k-th integer power of the ordinary Fourier transform" should actually be "When alpha is equal to an integer k times pi/2...", since alpha=pi/2 --> ordinary Fourier transform.
Likewise, in "Properties->coherence", shouldn't the intro text read "When a equals (pi/2)*k where k is an integer"?
(2) Notation:
For the fractional Fourier transform, is \mathcal{F}_\alpha or \mathcal{F}^\alpha preferred?
\mathcal{F}_\alpha is used in the start of the Definition section and in the Fractional kernel section, but \mathcal{F}^\alpha is used in much of the discussion on properties. This is particularly confusing given that a superscript notation \mathcal{F}^k is also used in this article to describe the ordinary Fourier transform.
For clarity, I would prefer \mathcal{F}_\alpha -- but I've just run across the FrFT and so don't know what the most common usage is. I only know that the article needs a common notation and that it's unclear to use the exact same notation for two related but different operators.
Gholleywiki (talk) 21:21, 21 April 2015 (UTC)
thread_title: "Integer powers"; also notation inconsistency

message: I guess that the Fractional Fourier Transform can be expressed using eigenfunctions and fractional powers of eigenvalues. Is that true? HenningThielemann (talk) 08:08, 31 May 2016 (UTC)
thread_title:  Eigenfunctions 

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thread_title:  External links modified 

message: Edit made to 'definition' section:
In the "Transform of a shifted function", the f_\alpha'(u) is likely supposed to be f_{\alpha'}(x)
given the contextual "where \alpha\not=\alpha'". I have made a modification, but am not an expert, so please review this change. If fine, feel free to delete this section from the talk page. Chalisque (talk) 18:27, 19 July 2018 (UTC)
thread_title:  Fixed probable typo 

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