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 <michaeldgodf...@gmail.com>: > 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 ------------------------------------------------------------------------------ Live Security Virtual Conference Exclusive live event will cover all the ways today's security and threat landscape has changed and how IT managers can respond. Discussions will include endpoint security, mobile security and the latest in malware threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ _______________________________________________ Octave-dev mailing list Octave-dev@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/octave-dev
