Signal estimation via selective harmonic amplification: MUSIC, redux

The technique known as multiple signal classification (MUSIC) is a semi-emp irical way to obtain pseudo-spectra that highlight the spectral-energy dist ribution of a time series. It Is based on a certain canonical decomposition of a Toeplitz matrix formed out of an estimated autocorrelation sequence. The purpose of this paper is to present an analogous canonical decompositio n of the state-covariance matrix of a stable linear filter filter by a give n time-series, Accordingly, the paper concludes with a modification of MUSI C. The new method starts with filtering the time series and then estimating the covariance of the state of the filter. This step in essence improves t he signal-to-noise ratio (SNR) by amplifying the contribution to the actual value of the state-covariance of a selected harmonic interval where spectr al lines are expected to reside. Then, the method capitalizes on the canoni cal decomposition of the filter state-covariance to retrieve information on the location of possible spectral lines. The framework requires uniformly spaced samples of the process.