[Numpy-discussion] zoom FFT with numpy? (Nadav Horesh)

Charles R Harris charlesr.harris@gmail....
Thu Mar 15 14:09:56 CDT 2007


On 3/15/07, Ray S <subscriber100@rjs.org> wrote:
>
> Hi Nadev,
> >A long time ago I translated a free code of chirp z transform (zoom
> fft)
> >into python.
>
> Thanks, I'll try it out.
>
> I did, however read before on the differences:
> From Numerix http://www.numerix-dsp.com/zoomfft.html:
> "One common question is : Is the zoom FFT the same as the chirp
> z-transform.
>
> The answer is : Absolutely not. The FFT calculates the FFT at N
> equally spaced points around the unit circle in the z-plane, the
> chirp z-transform modifies the locations of these points along a
> contour that can lie anywhere on the z-plane. In contrast, the
> zoom-FFT uses digital down conversion techniques to localise the
> standard FFT to a narrow band of frequencies that are centered on a
> higher frequency.


The points in the chirp z-transform can be densely spaced in the band you
are interested in, so it is probably closer to what you want to do. The same
effect can be obtained by zero filling, but that is probably not as
efficient unless you down sample first. Essentially, you will end up with
sinc interpolated points in the spectrum and you can just search for the
max.

BTW, did the s/n you gave refer to the signal or to it's transform?

Chuck
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