0
$\begingroup$

Say I open an audio segment with Audacity. Then I perform a size 4096+ FFT with a rectangular window. The program outputs bin magnitude values in dB. If I add them all together like this:

sum = 10*log10(10(bin1/10) + 10(bin2/10) + 10(bin3/10)...).

I get a value very close to the file's calculated "total RMS amplitude". (Or in this case, 3dB off since Audacity considers a full-scale square, instead of sine, to be 0dBFS).

Is this expected, a coincidence, or just an approximation?

Improve this question
$\endgroup$
1
  • $\begingroup$ I haven't Audacity's source code, but: Are you aware of Parseval's Theorem? $\endgroup$
    – Marcus Müller
    Commented Jul 13, 2019 at 9:37

1 Answer 1

Reset to default
2
$\begingroup$

This is expected and a consquence of Parseval's theorem.

Loosely speaking, it's a flavor of energy conservation: the total energy of the signal doesn't change when you transform it from the time domain into the frequency domain so the energy calculated in either domain must be the same.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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