Efficient Power Spectrum estimation using prewhitening and post coloring technique

The power spectrum estimation for a multichannel autoregressive process using prewhitened and postcoloring technique, which was originally developed for a single channel, is proposed. In order to make the extension, the Cholesky decomposition of the inverse autocorrelation matrix for a multichannel autoregressive process is discussed and the autoregressive model order selection for a multichannel process based on the exponentially em-bedded families criterion is introduced. The asymptotic mean and variance of the proposed estimator are derived. Compared to a filterbased autoregressive prewhiteneds multichannel power spectral estimator, the new estimator has less bias, i.e. higher resolution, and less overall mean square error for short data records due to the amelioration of end effects by the matrix prewhitener. It can serve as an excellent multichannel spectral estimator for processes exhibiting a wide dynamic range. Simulation results are given which show the advantage of the new estimator over a variety of common multichannel power spectral density estimators.