The technique known as multiple signal classification (MUSIC) is a semi-empirical way to obtain pseudo-spectra that highlight the spectral-energy distribution 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 decomposition of the state-covariance matrix of a stable linear filter driven by a given time-series. Accordingly, the paper concludes with a modification of MUSIC. 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 the signal-to-noise ratio (SNR) by amplifying the contribution to the actual value of the state-covariance of a selected harmonic interval where spectral lines are expected to reside. Then, the method capitalizes on the canonical 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.
Bibliographical noteFunding Information:
Manuscript received February 22, 1999; revised September 23, 1999. This work was supported in part by the NSF and AFOSR. The associate editor co-ordinating the review of this paper and approving it for publication was Dr. Lal C. Godara. The author is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA. Publisher Item Identifier S 1053-587X(00)01550-6.
- Canonical decomposition of state covariances
- Harmonic decomposition