Re: [OctDev] Octave in Google Summer of Code 2012

[Nir Krakauer]

Michael-- Thank you for the comments and references. The goal of this
project is indeed to create code that estimates frequency and phase
for unequally spaced and/or nonstationary data at FFT-like speed. I
hope that you will be able to continue to point us in the direction of
statistical rigor as the project develops.

Nir



2012/4/23 Michael D Godfrey <address@hidden>:
> 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