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?
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$\begingroup$ It is called the Chirp-Z-Transform. $\endgroup$– SpaceyMar 4, 2013 at 20:06
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$\begingroup$ @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. $\endgroup$– endolithMar 4, 2013 at 21:25
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$\begingroup$ @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. $\endgroup$– SpaceyMar 4, 2013 at 22:07
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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.
