Talk:Trigonometric interpolation

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[edit] Errors in article

Due to the Stone-Weierstrass theorem this function exists and is unique. It is called complex trigonometric polynomial of degree N-1 and has the form ...

I don't think this article is correctly worded. First of all, a continuous function is certainly not uniquely determined by the requirement that it pass through n specified points, nor is this false statement implied by the Stone-Weierstrass theorem. The correct statement is more along the lines of, if you are looking for a periodic interpolating function of the given trigonometric form, then the coefficients are uniquely determined. However, even this is a bit too simplistic because there are multiple possible choices of trigonometric interpolation polynomial due to aliasing. See e.g. the discussion under discrete Fourier transform.

I don't have time to make this article not suck right now, but I thought I should tag it to warn readers, at least. —Steven G. Johnson 23:44, 12 December 2005 (UTC)

Ouch. I remember that I noticed this some time ago, but I postponed action first and forgot about it later. By the way, Stone-Weierstrass has nothing to do with it. I think {{disputed}} is still too weak, so I commented out most of the article (false info is worse than no info). Hopefully, I'll find time soon to fix it, if Steven hasn't done so before. -- Jitse Niesen (talk) 00:10, 13 December 2005 (UTC)