Often times in signal processing discussions people talk about the number of points of the fft (eg, 512, 1024, 2048), and they also talk about the number of bits of the signal. Another important part of the discussion should be the signals of interest. For example, if one is really interested in signals below 60Hz, it seems wasteful for an FFT algorithm to test for power at higher frequencies (and Fourier coefficients?). Is this the case in common implementations of the FFT algorithm? This savings could be quite relevant to someone performing an FFT on a low-powered microcontroller.
1 Answers
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You could low-pass filter, decimate, and use a shorter FFT. But if the cost of quality filtering is a large fraction of NLogN, it (plus the shorter FFT) may cost as much as just doing the longer FFT and throwing away unneeded result bins.
You could use a Goertzel filter for just the needed DFT result frequency bins, but again, if you need around LogN result bins or more, an optimized full FFT may cost less computation (and also be slightly more accurate). So this is mainly useful if you need a lot less result bins than log(N), such as with DTMF decoding using a slow microcontroller.
