statistical jargon (UNCLASSIFIED)

[Mullins, Bill AMRDEC]

Classification: UNCLASSIFIED
Caveats: NONE



>
> While I agree with most of what's been written so far, my initial
point
> is that there are at least two other uses of "spectral analysis" as a
> purely mathematical term that has nothing to do with chemistry,
> astronomy or physics (although, obviously, it can be used for those
> purposes).


I meant for my comment to include mathematical spectra as well as
physical ones. (Image processing as opposed to audio equalization, for
example).

>
> Wiki specifically connects the disambiguation of "Spectral analysis"
to
> Spectral Theory (Banach spaces, etc., in functional analysis) in
> mathematics and to Spectral Density Estimation in statistics. Both are
> quite distinct from the "pure physical sciences" meaning of spectrum,
> which they define internally.
>
> Here's the statistics entry:
>
> > In statistical signal processing, the goal of spectral density
> > estimation is to estimate the spectral density (also known as the
> > power spectrum) of a random signal from a sequence of time samples
of
> > the signal. Intuitively speaking, the spectral density characterizes
> > the frequency content of the signal. The purpose of estimating the
> > spectral density is to detect any periodicities in the data, by
> > observing peaks at the frequencies corresponding to these
periodicities.
>
> These are not covered under the OED definition at all. So it's not
just
> a question of emphasis. In Tukey's case, he was one of the inventors
of
> spectral analysis in statistics, which is why his name shows up in the
> quotation in the OED.
>

No, but they would be covered under what I proposed.  Any time-varying
function can be decomposed spectrally, and then analyzed.  It is a
mathematical process, which can be implemented into the physical world.
Classification: UNCLASSIFIED
Caveats: NONE

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