9
$\begingroup$

If I recall correctly, there is a variation of the DFT that can be used to analyze a specific band of the spectrum of a signal. How is it called?

$\endgroup$
  • $\begingroup$ It is called the Chirp-Z-Transform. $\endgroup$ – Spacey Mar 4 '13 at 20:06
  • $\begingroup$ @Mohammad: "One common question is : Is the zoom FFT the same as the chirp z-transform. The answer is : Absolutely not." numerix-dsp.com/zoomfft.html Would be a good answer to explain the relationship. $\endgroup$ – endolith Mar 4 '13 at 21:25
  • $\begingroup$ @endolith Not the same sure, but they are different ways of arriving at the same end result. The 'Zoom-FFT' involves downsampling / BPF / FFT, whereas the Chirp-Z Transform evaluates the Z-transform on the band you want. I have heard people refer to 'Chirp-Z' as 'Zoom-FFT' as in its particular application. $\endgroup$ – Spacey Mar 4 '13 at 22:07
9
$\begingroup$

You're probably referring to the zoom FFT. It's essentially a technique that allows for complexity reduction in the case where you have a small portion of a larger band that you'd like to analyze at high spectral resolution. It prevents you from having to calculate the high-resolution frequency content in the bands that you don't care about. Roughly, the algorithm can be summarized as follows:

  • Apply a bandpass filter around the region of interest, eliminating the components outside the band that you care about.

  • Decimate the signal by a factor $D$, such that the resulting sample rate still meets the Nyquist criterion for the filter's passband width. Depending upon where the band's center frequency was, this process might also involve frequency-translating the signal to baseband.

  • Perform a DFT on the signal. In order to get the same frequency resolution at the output, the "zoomed" transform only requires a transform length that is $\frac{1}{D}$-th of what you would need to use if you used the original, unfiltered signal for your analysis.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.