CrossCorrelationTable

One of the types of objects in Praat. A CrossCorrelationTable represents the cross-correlations between a number of signals. Cell [i,j] of a CrossCorrelationTable contains the cross-correlation between the i-th and the j-th signal. For example, the CrossCorrelationTable of an n-channel sound is a n×n table where the number in cell [i,j] is the cross-correlation of channel i with channel j (for a particular lag time τ).

A CrossCorrelationTable has a square matrix whose cells contain the cross-correlations between the signals and a centroid vector with the average value of each signal.

Remarks

Sometimes in the statistical literature, the cross-correlation between signals is also called "covariance". However, the only thing a Covariance has in common with a CrossCorrelationTable is that both are symmetric matrices. The differences between a CrossCorrelationTable and a Covariance are:

1. A Covariance matrix is always positive-definite; for a cross-correlation table this is only guaranteed if the lag time τ = 0.
2. The elements cij in a Covariance always satisfy |cij/√(cii·cjj)| ≤ 1; this is generally not the case for cross-correlations.

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© djmw, September 8, 2017