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[Octave-bug-tracker] [bug #31474] autocor.m & autocov.m are wrong

From: Reginald Beardsley
Subject: [Octave-bug-tracker] [bug #31474] autocor.m & autocov.m are wrong
Date: Thu, 28 Oct 2010 16:57:30 +0000
User-agent: Mozilla/5.0 (X11; U; SunOS i86pc; en-US; rv: Gecko/20080520 Firefox/

Follow-up Comment #7, bug #31474 (project octave):


Out of curiosity I did some research.  It turns out I was both right and
wrong at the same time.

Friedrich Leisch is a statistician.  In one of the perverse accidents of
mathematics, the statisticians have very different definitions for
autocorrelation and autocovariance than commonly used in the signal processing
community.  While I have a few statistically oriented texts, they are not
where I learned the mathematics.  If I was ever aware of the discrepancy, it
was forgotten long ago.

The presence of autocor.m and autcov.m in the signal directory led me to
expect a signal processing discipline definition as presented by:

Random Data
Bendat & Piersol

Digital Signal Processing
Oppenheim & Schaefer

Theory and Application of Digital Signal Processing
Rabiner & Gold

The Fourier Transform & its Applications

The Fourier Integral & its Applications

and many more.

In all of these, the autocorrelation is the inverse Fourier transform of the
power spectrum and the autocovariance is the inverse Fourier transform of the
power spectrum w/ the DC component set to zero.  If the peak values are
normalized to 1 it is explicitly described as "normalized".

However, Box & Jenkins in "Time Series Analysis" defined the autocorrelation
and autocovariance as implemented by Friedrich Leisch.

Rather than using my "corrected" versions, I'd like to suggest that the
documentation for autocor(), autocov() and periodogram()  explicitly  note
that they implement the Box & Jenkins definitions rather than the Oppenheim &
Schaefer/Bendat & Piersol definitions.

All of Leisch's contributions probably belong in the statistics directory,
however, most are unlikely to be used by anyone other than a statistician, so
there is little risk of confusion.

Have Fun!


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