On 04/23/2012 04:53 PM, Jordi Gutiérrez Hermoso wrote:
Benjamin Lewis (ben_zen in #octave) will work with Nir Krakauer on
creating a least squares spectral analysis toolbox for Octave-Forge.
Ben is a strong student who has demonstrated the ability to work
independently and absorb sophisticated concepts quickly.
I thought about offering to mentor this project, but my available time
would have made it hard for me to contribute much. However, I would
like to make a few "starting" comments.
1. Standard methods of spectrum estimation are, of course, least
squares methods. John Tukey's paper on spectrum analysis viewed
as analysis of variance helps make that clear.
2. The currently interesting problems, as some the the "least squares"
people point out, concern less general, but important, problems like
dealing with unequally spaced data, or special interest in some
frequency-
specific features, or as a serious data compression technique.
I assume that some of this is a main focus of the project.
3. Speaking as a statistician, could I encourage looking at the statistical
literature in addition to areas such as geophysics, quantum physics,
biomedical applications, etc. The statisticians, such as Tukey,
Brillinger,
Parsen, Hannan, Rosenblatt, and others have tended to take a more
careful interest in the statistical behavior of the computed
results. This
is important. Ever since Schuster, serious errors have been made
by not
understanding the statistical behavior of the estimates. Any effective
package should provide reliable estimates of the variability of the
estimates.
4. Could I also add that both unequally spaced data and non-stationarity
are important and often related problems. Techniques that deal
with both will be
particularly helpful. Complex-demodulation (physicists tend to call
this the
complex heterodyne technique (CHT)) is increasingly being used for
large-
scale problems, including for example LIGO. This technique lends
itself
well to both unequally spaced data and non-stationarity, and can also be
used to compose higher-order spectrum estimates and for, for example,
extrapolation.
5. Finally, I have to admit that I think that an early paper written by
Kit Bingham,
myself, and John Tukey is still relevant. John wrote the FFT part
and I wrote
(with lots of help from John) the complex-demodulation part. This
is pretty
easily found on the web searching on something like tukey godfrey
modern
techniques... Originally, this was an IEEE publication. The copy
on my web
site has a (very) few minor corrections and, as a PDF, may be easier
to read.
I would be interested to see how this develops, and offer help as possible.
This can definitely add a lot to the tools available to the Octave
community.
Have fun!
Michael Godfrey
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