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I have a question which is closely related to this one: FFT Processing Gain

^that discussion is a bit general so I want to ask a very objective question to see if I can apply that knowledge:

If I collect one million time samples and perform a one million point DFT, roughly what DFT processing gain (in dB) improvement can I expect to achieve in pulling a weak spectral component up above background noise in comparison to a 100 point DFT?

I guess that answer is 100,000. isn't it?

we have 9999910 more bins.

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    For a single sinusoid, the link in the FFT processing gain discussion suggests a gain of: $10log_{10}(M/2)$. – learner May 25 '14 at 07:27
  • So, to be explicit, in the example i was considering would it be: 10log10(1,000,000/2)

    M is the number of DFT bins right? I always see M written as the frequency bin number being considered.

    So I just do that 10log10(m/2) calculation for both sizes and then compare them?

    is that correct?

     –  May 25 '14 at 11:23
  • Yes, M is the total number of bins. You are right, do the calculation for both sides and compare them. What I think is that gain is valid only for a single tone. You might prove me wrong. – learner May 25 '14 at 12:29
  • Please forgive me but I don't quite understand, what does that mean, 'gain is valid only for a single tone' ? –  May 25 '14 at 12:40
  • you mean for a single frequency component and not for the number of DFT points being considered as a whole? –  May 25 '14 at 13:12
  • Gain is valid if in time domain I've only a single tone. More DFT points I collect, more gain I've. But for a wide-band signal, or for example, OFDM, this might not hold. – learner May 25 '14 at 13:28

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