## autocorrelation

### autocorrelation

> Hello
> we need some information about autocorrelation and fractionnal pitch In
> fact we search an algorithme for recognition of a notes in a monody (one
> note after another)
> Thanks

The book 'Digital Processing of Speech Signals' by Rabiner and Gold
covers this topic in depth (Prentice Hall). It is considered a standard
literature for pitch detection.

Stephan
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Director, Research & Development
Prosoniq Products Software GmbH, Audio Research & Development
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### autocorrelation

Hello
we need some information about autocorrelation and fractionnal pitch In
fact we search an algorithme for recognition of a notes in a monody (one
note after another)
Thanks

Let  x[n] = s[n] + p[n]
where s[n] is complex Gaussian white noise (GWN)  and p[n] is a
complex signal in the for Ae^{j2pi w + phi} where w is radian
frequency and phi is a phase factor.
I want to show that if I do the autocorrelation of x[n]  (ie
x[n]x[n-1]* , where * denotes the complex conjugate) that the argument
will more closely approach the actual frequency of p[n],
so, if I did  the autocorrelation of x[n] and then took the argument
of the result, it would be with in some % of  the true frequency.
You can assume that the mean of the GWN is zero and the variance is
0.1 or whatever is convenient.

I have taken x[n]x[n-1]* and multiplied it out...and you can make a
few assumptions to limit terms, but I am not seeing a good way to show
what is happening w/ the argument.

Thanks
Craig