# Talk:Time–frequency representation

WikiProject Statistics (Rated Start-class, Mid-importance)

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WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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Field:  Probability and statistics

Whoever created this page did a nice job. Solid information and well written. jeffo 14:50, 29 Jul 2004 (UTC)

Examples, formulas, and perhaps sample images would be of benefit. The article in its current form seems to appeal mostly to people already familiar with the subject. A good start, though. Rethunk 20:06, 8 Jun 2005 (UTC)

I wrote this page. Thanks. I put a lot of time and effort into writing a thorough introduction to the subject in [http:// www.ffconsultancy.com/free/thesis.pdf my PhD thesis]. I also contributed significantly to research in this area (see the Hilbert-Hermitian wavelet) and commercialized my work in the form of [http:// www.ffconsultancy.com/products/CWT/ a Mathematica add-on]. If you want to do time-frequency analysis accurately, the maths gets very hard very quickly. So I'm not sure it belongs on Wikipedia. Maybe a cutdown version based on Gabor/Morlet would be ok. Jon Harrop 13:31, 15 April 2007 (UTC)

## Empty Set

If I am not mistaken, the set ${\displaystyle {\mathcal {C}}}$ in the paragraph named Quadratic forms is always convex as it is always empty. I do not the correct version of this statement, I am guessing that it should read something like If for every ${\displaystyle T\in [0,E_{0}]}$ the set ${\displaystyle \{(t,f)\in \mathbb {R} ^{2}:|E(t,f)|>T\}}$ is convex, then the QTFR ${\displaystyle E(t,f)}$ is cross-term free.

46.142.36.29 (talk) 22:48, 21 June 2014 (UTC)

Yea, I agree, the set ${\displaystyle \{(t,f)\in \mathbb {R} ^{2}:|E(t,f)|>T,\,\forall T\in [0,E_{0}]\}}$ is always empty since ${\displaystyle |E(t,f)|\leq E_{0}=\sup E(t,f)}$. I don't know what the correct version is, and I wasn't able to find it in Jon Harrop's thesis, but I think your suggestion of pulling the "for every ${\displaystyle T\in [0,E_{0}]}$" out of the set comprehension is the most sensible thing to do. -- Tuckerleavitt (talk) 01:54, 25 September 2017 (UTC)