If one considers what the formulae actually say, it becomes clear that really has length at least , because all indices between and inclusive are used at least once. It is true than an implementation could make do with making bn a vector of length N since , but that is an optimisation that is inappropriate to make that early in the text, since it makes the text confusing.
A better approach would probably be to consider and both as defined for all , but with for and , and possibly for . Then the convolution becomes a straightforward (linear) convolution, and it is clear that it can be computed as a periodic convolution of sufficient length M. The shortest length that suffices is , but the idea of the algorithm is that one can instead pick a slightly larger M for which there is an efficient FFT using some more basic algorithm. 22.214.171.124 (talk) 21:03, 18 September 2012 (UTC)
The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.
The result of the move request was: moved to Chirp Z-transform. The main article Z-transform contains the hyphen, as well as few reference works I checked (i.e. Mathworks), so it seems to fit (NAC). No such user (talk) 12:39, 19 January 2015 (UTC) No such user (talk) 12:39, 19 January 2015 (UTC)
Bluestein's FFT algorithm → Chirp Z-transform – This article confuses me. In the same sense that the FFT is a particular implementation of the DFT, it would seem that the CZT is a general transform that can be implemented in different ways, and the Bluestein algorithm is a particular implementation (and there's probably a slow, direct implementation?) The CZT computes samples in spirals around the Z plane, and the DFT and "zoom-FFT" are special cases of the CZT that you get when setting the parameters so that it only loops around the unit circle. I think the article should be about the chirp-Z transform, and the Bluestein algorithm should be a section in that article. If it was originally formulated as an DFT algorithm, and the more general Chirp-Z was invented later, that should be mentioned, but the article should be about the transform, not the history. (And it should have a picture of the spiral samples.) — Omegatron (talk) 21:21, 17 December 2014 (UTC)
Support – I've never heard of Bluestein's algorithm, but the article says it's commonlky called the chirp Z transform, so seems OK. Except it's not clear what's the best "styling", since sources are all over on where to put the hyphen, or to use zero or two hyphens, and whether to capitalize the z. Something we can tweak later... Dicklyon (talk) 01:11, 18 December 2014 (UTC)
My instinct is to say the hyphen should be omitted, under the convention of WP:HYPHEN. "Z transform" is a compound noun, not a compound modifier. However, I do notice that Z-transform is hyphenated on Wikipedia. (I don't notice that the question was ever discussed on its Talk page.) —BarrelProof (talk) 05:09, 18 December 2014 (UTC)
I agree that the sometimes-seen convention of a hyphen in letter-thing is odd in English; but not rare. In this case, my intuition is that the type of transform is "chirp-z", and that that's where the hyphen belongs. But look how mixed sources are. Dicklyon (talk) 05:21, 18 December 2014 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.