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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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    $\begingroup$ For a single sinusoid, the link in the FFT processing gain discussion suggests a gain of: $10log_{10}(M/2)$. $\endgroup$ – learner May 25 '14 at 7:27
  • $\begingroup$ 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? $\endgroup$ – user8769 May 25 '14 at 11:23
  • $\begingroup$ 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. $\endgroup$ – learner May 25 '14 at 12:29
  • $\begingroup$ Please forgive me but I don't quite understand, what does that mean, 'gain is valid only for a single tone' ? $\endgroup$ – user8769 May 25 '14 at 12:40
  • $\begingroup$ you mean for a single frequency component and not for the number of DFT points being considered as a whole? $\endgroup$ – user8769 May 25 '14 at 13:12

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