Talk:Chirp Z-transform

This article has been mentioned by a media organization:

"A DSP Algorithm for Frequency Analysis". Embedded Systems Programming. January 15, 2004.

This page was also cited as a source in the following academic paper:

Igor Aizenberg and Jaakko T. Astola, "Discrete Generalized Fresnel Functions and Transforms in an Arbitrary Discrete Basis," IEEE Transactions on Signal Processing 54 (11), pp. 4261-4270 (2006).

Dubious

If one considers what the formulae actually say, it becomes clear that $b_{n}$ really has length at least $2N-1$ , because all indices between $-(N-1)$ and $N-1$ inclusive are used at least once. It is true than an implementation could make do with making b_n a vector of length N since $b_{-n}=b_{n}$ , 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 $a_{n}$ and $b_{n}$ both as defined for all $n\in \mathbb {Z}$ , but with $a_{n}=0$ for $n<0$ and $n\geq N$ , and possibly $b_{n}=0$ for $|n|\geq N$ . 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 $M=2N-1$ , 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. 81.170.129.141 (talk) 21:03, 18 September 2012 (UTC)[reply]

Requested move 17 December 2014

The request to rename this article to Chirp Z-transform has been carried out.

If the page title has consensus, be sure to close this discussion using {{subst:RM top|'''page moved'''.}} and {{subst:RM bottom}} and remove the {{Requested move/dated|…}} tag, or replace it with the {{subst:Requested move/end|…}} tag.

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)[reply]

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)[reply]