**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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## Correlation

Definition:Thecorrelation operatorfor two signals and in is defined as

We may interpret the correlation operator as

which is the coefficient of projection onto ofadvancedby samples (shifted circularly to theleftby samples). The time shift is called the correlationlag, and is called alagged product. Applications of correlation are discussed in §8.8.