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For example, when playing piano, at the same time, print out the key notes by analyzing the signal of piano sound.

How to do some pre-processing to remove the noise? When calculate with FFT, noise will influence the result?

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  • $\begingroup$ Noise is surely a problem when there are significant amounts of it present. But for polyphonic pitch detection it's probably very low on the priority list. The task you're attempting is hard, even very hard, and there's no simple recipe for it. $\endgroup$
    – Jazzmaniac
    Sep 6 '14 at 8:08
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There is no easy answer to that question. Plenty of algorithms exists which are suitable to that task. Nowadays Non-negative Matrix Factorisation (NMF) is getting more and more popular in this field of research. If you have enough of resources and knowledge then you can try it. It's just a 'fancy' SVD decomposition with some 'constraints and tweaks'.

Some literature for you that might be useful in terms of choosing the approach. First one contains some vast overview of the problem as well as lot's of references:

Benetos E., et al. - Automatic music transcription: challenges and future directions

Benetos E., Dixon S. - Joint Multi-pitch Detection using Harmonic Envelope Estimation for Polyphonic Music Transcription

Benetos E., et al. - Automatic Transcription of Pitched and Unpitched Sounds from Polyphonic Music

Benetos E. - Automatic Transcription of Polyphonic Music Exploiting Temporal Evolution - PhD Thesis

O'Hanlon K., Plumbley M. - Automatic Music Transcription using Row Weighted Decompositions

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    $\begingroup$ heh! another treatise on pitch detection (this time polyphonic). thanks for the links. lotsa reading to do. do you know this Benetos guy? i wonder if he studied under Mark Sandler (or is that King's College?) $\endgroup$ Sep 7 '14 at 21:39
  • $\begingroup$ @robertbristow-johnson: I believe he worked with Simon Dixon mostly. Although Mark Sandler is indeed a professor on QMUL. $\endgroup$
    – jojek
    Sep 8 '14 at 7:14
  • $\begingroup$ Hi @robertbristow-johnson. I did some yt search and I found a video of Benetos doing a talk about NMF. Quite interesting. Here is the link. $\endgroup$
    – jojek
    Apr 12 '16 at 6:57
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Pitch detection/estimation is different from FFT peak frequency estimation. The "noise" you may be seeing in the FFT result could instead be harmonic components of the spectral structure of the pitched note, thus should not be filtered out, as they may be important to creating the perception of pitch.

Try a pitch detection or estimation algorithm instead of a peak frequency estimator.

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