Path: utzoo!attcan!uunet!world!decwrl!ucbvax!ucsd!sdcc6!am299aw
From: am299aw@sdcc6.ucsd.edu (Gregory Breit)
Newsgroups: comp.dsp
Subject: Re: Practical DSP problem
Summary: How about a Linear Least Squares???
Keywords: Prony Spectral Line Estimator
Message-ID: <13216@sdcc6.ucsd.edu>
Date: 12 Oct 90 00:46:49 GMT
References: <5169@hemuli.tik.vtt.fi> <3594@syma.sussex.ac.uk>
Organization: University of California, San Diego
Lines: 38

In article <3594@syma.sussex.ac.uk> paulr@syma.sussex.ac.uk (Paul T Russell) writes:
>
>We don't know the absolute phase of the signal but we do know the
>exact frequency. We are generating two sine waves at frequencies
>f1 and f2 and trying to measure the distortion product at 2f1 - f2.
>The signal is swamped by the two much larger components at f1 and
>f2, and is close to the noise level. 

An approach you might consider would be to use a variation on the
Prony Spectral Line Estimator.  The PSLE is especially well suited
for spectral analysis of signals containing a finite number of
discrete sinusoids.  Check out these papers:

Meyer, et al, The Prony Spectral Line Estimation (PSLE) Method for
the Analysis of Vascular Oscillations.  IEEE Trans. Biomed. Eng.
36(9), 968-971, 1989.

Kay, SM, and SL Marple, Spectrum Analysis--A Modern Perspective.
Proc. IEEE, 69(11), 1380-1419, 1981.

Also, Marple's new book on spectral analysis (I don't remember the
title) has a chapter on this stuff.

The PSLE is basically a two-step process which utilizes a clever
linearization of the problem of fitting a finite # of sinusoids to
a signal.  The first, and most complicated step actually determines
the frequencies themselves (which you already know).  The second
step is merely a linear least squares fit of those frequencies to
the data.  The complex amplitude you get from that step allows you
to determine the best combination of amplitude and phase which fits
the data.  You might find it useful to apply a linear least squares
to find the most likely amplitude of your sinewave buried in noise.
LLS is a pretty common problem, you should be able to find some
source code.  Good luck.

Gregory Breit
Department of Applied Mechanics and Engineering Sciences, UCSD
am299aw@sdcc6.ucsd.edu