Talk:Prolate spheroidal wave function

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Contrary to what the first paragraph claims, the PSWFs are not time-limited. If $\psi _{n}$ were in fact time-limited, the second $Q_{T}$ in the expression $Q_{T}P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}$ would be redundant anyway. Based on the original paper by Slepian and Pollack, and using the notation established in this article, the correct expression seems to be

P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}

where $\psi _{n}$ are bandlimited. Perhaps somebody with more background in this matter can confirm this. Qopzm (talk) 00:39, 8 July 2010 (UTC)[reply]

I agree

I agree with this observation, that the PSWF's are not time limited. In fact, they are defined to be those functions which maximise the power contained the region [-T,T] given the constraint that they have unit power on R. I have constructed explicitly these functions and they do not vanish outside a compact interval. Indeed, it is a general result that a function which vanishes on a compact interval necessarily cannot have a frequency content which vanished on a compact interval. I will work on the revision to this incorrect material. angusprain 18:25, 1 March 2013.

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Order of material

It seems natural to me to start the article with the context from the spheroidal wave equation/spheroidal coordinates. This is where the name comes from. The application to band-limited Fourier analysis then later, as an additional application. DieHenkels (talk) 10:48, 7 May 2021 (UTC)[reply]