Re: Octave in Google Summer of Code 2012

[Michael D Godfrey]

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