Finding the strongest beat in a sound wave using autocorrelation

In summary, the conversation discusses the use of autocorrelation to find the saliency of each beat in a sound wave representing a piano piece played at a steady tempo. The speakers also mention the difficulty of finding a clear beat in music and suggest alternative methods such as finding changes in frequency content or using beat detection algorithms. They also mention examples of converting audio recordings into music notation and using DSP for this task.
  • #1
wildetudor
22
0
Hi everyone,

I have a sound wave representing a piano piece played at a steady tempo, and would like to get a graph of the saliency of each beat (essentially, a probability distribution for how strong each possible tempo is). I understand that this is done by plotting the autocorrelation function, however I don't quite understand why a graph of r coefficients against each possible lag value (which is, as far as I understand, the deffinition of an autocorrelogram) would have anything to do with beats.

The following Matlab code produces a graph that doesn't in any way suggest anything to do with the actual steady beat of the piece (60 BPM):

Code:
[y,Fs] = wavread('d:\bach.wav');
[r,lags]=xcorr(y,'coeff');  
plot(lags,r)

Clearly I'm understanding autocorrelation wrongly. For instance, in this very simple example, the frequency of the sine hidden in noise is nowhere visible from the autocorrelation graph - or is it? Furthermore, that frequency would actually be the pitch of the sound, and not any rhythm-related measure!

The MIR toolbox for Matlab has a function specifically for finding the tempo of a waveform - however what I'm after now is understanding these things at a theoretical level.

Anticipated thanks for any clarifications!
 
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  • #2
wildetudor said:
For instance, in this very simple example, the frequency of the sine hidden in noise is nowhere visible from the autocorrelation graph - or is it?
You can see a clear sine wave in the autocorrelation function, which corresponds to a "hidden" sine wave in the original function with a period of ~10.

Furthermore, that frequency would actually be the pitch of the sound, and not any rhythm-related measure!
Can you find the time steps where the frequency in the signal changes? An autocorrelation of that should help.
Alternatively, search for steps in the autocorrelation function, this could help as well.
 
  • #3
Problem with music is that it can be very subtle. However, to find an 'obvious beat', why not find the short term RMS values (Energy with time) of a long passage and FFT that to find low frequency (sub Hz) energy variations. Some pre-filtering could identify components like cymbal strikes or bass drum beats. (Sound to light 'disco' boxes do this quite well)
 
  • #4
Thanks for your replies! I'm afraid I still don't fully understand, though, the link between a time signal's (waveform's) periodicity and its autocorrelation function; and, I could also add, the link between the signal's autocorrelation function and its Fourier transform (the latter of which I understand how it relates to pitch but not to rhythm)
 
  • #5
wildetudor said:
Thanks for your replies! I'm afraid I still don't fully understand, though, the link between a time signal's (waveform's) periodicity and its autocorrelation function; and, I could also add, the link between the signal's autocorrelation function and its Fourier transform (the latter of which I understand how it relates to pitch but not to rhythm)

The rhythm would correspond to peaks in level (rectified and integrated?) and the rate at which they repeat. That's why I included the idea of "sub Hz".

I am not sure that the ACF would necessarily reveal the rhythm unless there were rhythmic repeats of the same instrument producing a note that was somehow phase consistent? It could be worth while trying with some actual examples of music.
 
  • #6
Thanks, that's quite helpful, I'll play around with it in Matlab on my own a bit to facilitate intuition :)
 
  • #7
The autocorrelation for the audio of a complete piano piece probably won't show anything useful.

If you calculate autocorrelations for short "windows" of the data, you might be able to see the CHANGES in frequency content at the start of each new note. But even a single note on a piano is far from being a simple sine wave, and most piano music has several notes at different pitches sounding at the same time, so this isn't going to be easy to see.

There are a few commercial computer programs that claim to be able to convert an audio recording into music notation, for example http://www.neuratron.com/audioscore.htm, but they don't work very well for anything except very simple audio, like a single instrument that can only play one note at a time.

But it is possible ... http://www.ted.com/talks/john_walker_re_creates_great_performances.html
 
  • #8
If your task is to find a reliable method using DSP and not a brain, it will fall over for some examples, I'm sure. It would depend on how good it needs to be. Good luck and have fun.
 
  • #9
better look up "beat detection" which is a similar problem to pitch detection. i would suggest googling jean larouche beat detection without quotes and reading any number of documents this guy wrote.

it ain't an easy problem.
 

What is autocorrelation and how is it used in finding the strongest beat in a sound wave?

Autocorrelation is a mathematical technique used to measure the similarity between a signal and a time-shifted version of itself. In finding the strongest beat in a sound wave, autocorrelation is used to identify repeating patterns in the sound wave and determine the dominant frequency or beat.

How does autocorrelation differ from other methods of finding the strongest beat in a sound wave?

Unlike other methods, such as Fourier analysis, autocorrelation does not require prior knowledge of the signal's frequency components. It is also less sensitive to noise and can accurately detect the dominant beat even in complex and noisy sound waves.

Can autocorrelation be used for any type of sound wave?

Yes, autocorrelation can be applied to any type of sound wave, including music, speech, and environmental sounds. However, it may be less effective for highly irregular or non-repetitive sounds.

What are the limitations of using autocorrelation to find the strongest beat in a sound wave?

Autocorrelation may struggle to accurately identify the strongest beat in a sound wave if the beat is weak or if there are multiple strong beats present. It also requires a certain level of periodicity in the signal, which may not be present in some types of sounds.

Are there any potential applications for using autocorrelation to find the strongest beat in a sound wave?

Yes, autocorrelation has various applications in fields such as music analysis, speech recognition, and biomedical signal processing. It can also be used in audio editing software to automatically detect and align beats in music tracks.

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