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I want to program a microcontroller in C but I am asking about the theoretical aspect of it. I think I've got an idea what I am going to do but there is one thing I can't quite get. To begin with, I will use a guitar, so there is a 82Hz-987Hz range. So roughly, I'm going to low-pass the data on 1KHz, "window" them and apply FFT. Supposedly, I am going to have a good estimate.

Since highest frequency is ~1KHz, I decided my sample rate to be 2KHz (haven't tested yet if it works).

Suppose I have a 2 seconds track with 1 note each second. If the first note is C, my result would be 2000 C notes for the first second right? We can say that every time there is a note change, that's when you recognize a note, so if the second note is D, the program will acknowledge C, then D (and not 2000 times C and 2000 times D). The problem I see, is that if the second note is also C, how would I know that indeed there is a note hitting?

I believe I need an extra step to the process but I can't quite find what would that be. Might be that I have to go a different route though.. (if this is the case just mention the method, no need to elaborate on it and lose your time, I will read about it).

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Hotpaw2's reply addressed the note boundary detection problem (envelope tracking is a solution, though they are more robust solutions, look for "onset detection"). A few more comments on your plan:

  • Sampling your signal at 2kHz is going to cause more problems than it is going to solve. The signal from the guitar is not a pure sine wave, so there are harmonics above 1kHz that will be aliased if not filtered properly. This would require very steep anti-aliasing filters, with a very narrow transition band.

  • You have not explained how you intend to compute pitch, but it is very unlikely that your pitch detection method is going to yield a result for every single input sample. More likely, you'll have to find a trade-off (for example through the choice of a FFT or autocorrelation size; or a bandpass filter Q factor) between how often you get a pitch estimate, and how accurate this estimate is.

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  • $\begingroup$ This is a beginner's project so I am still grasping the basic concepts, that means some of my assumptions could be wrong. 1) About the sample rate, since I am already low-passing the sound at 1Khz it is going to eliminate the majority of harmonics over 1KHz. I just want to find the fundamental frequency and I don't need to reconstruct the signal so I assume that this sample rate won't be much of a problem. $\endgroup$
    – user2832080
    Commented Oct 11, 2013 at 17:47
  • $\begingroup$ 2) I was thinking that I can just find the peak frequency in each of my sample and then somehow I will find when a note is hitting. Granted, it isn't the best method but it's quite simple and the results will be terrible. I haven't tried programming it but playing with sounds and frequency domains on my PC, I can see with naked eye that most times the fundamental frequency is the one peaking. $\endgroup$
    – user2832080
    Commented Oct 11, 2013 at 17:49
  • $\begingroup$ Which filter do you use to limit the bandwidth to 1kHz? How do you determine "the peak frequency" from just one single sample? $\endgroup$
    – pichenettes
    Commented Oct 11, 2013 at 18:30
  • $\begingroup$ I am thinking RC filter before ADC. More like the peak frequency each time division. What would be a good time division length in order to apply the window function and FFT? $\endgroup$
    – user2832080
    Commented Oct 11, 2013 at 21:06
  • $\begingroup$ A simple RC filter will only attenuate harmonics, not eliminate them; so they will all be aliased in your 1kHz band and you'll get false readings. FFT is just not the right tool for note detection. $\endgroup$
    – pichenettes
    Commented Oct 12, 2013 at 7:34
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Usually, the envelope of a note will decay. A new note pluck will start (add or replace) a new amplitude envelope with an attack transient.

So you might add envelope tracking to your spectral frequency analysis (which may or may not be appropriate for correct pitch estimation).

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