# [Numpy-discussion] Zoom fft code

Stéfan van der Walt stefan@sun.ac...
Mon Jan 5 07:58:11 CST 2009

2009/1/5 Neal Becker <ndbecker2@gmail.com>:
> I was not aware that chirp-z transform can be used to efficiently compute DFT over a limited part of the spectrum.  I could use this.  Any references on this technique?

The only reference I have is the one mentioned in the source:

Rabiner, L.R., R.W. Schafer and C.M. Rader.
The Chirp z-Transform Algorithm.
IEEE Transactions on Audio and Electroacoustics, AU-17(2):86--92, 1969

The discrete z-transform,

X(z_k) = \sum_{n=0}^{N-1} x_n z^{-n}

is calculated at M points,

z_k = AW^-k, k = 0,1,...,M-1.

You can think of the z_k's as a spiral, where A controls the outside
radius (starting frequency) and W the rate of inward spiralling.

Regards
Stéfan