Signal estimation via selective harmonic amplification: MUSIC, Redux

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.