Welch Autocorrelation Estimate

Since
which is *circular* (or
cyclic) correlation, we must use *zero padding* in each FFT in
order to be able to compute the acyclic autocorrelation function as
the inverse DFT of the Welch PSD estimate. There is no need to
arrange the zero padding in zero-phase form, since all phase
information is discarded when the magnitude squared operation is
performed in the frequency domain.

The Welch autocorrelation estimate is *biased*. That is, as
discussed in §6.6, it converges as
to the true
autocorrelation
weighted by
(a Bartlett window). The
bias can be removed by simply dividing it out, as in
(6.15).

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University