Positive-definite Toeplitz embedding based on the cyclic extension of a data matrix

Embedding in a block-Toeplitz matrix is one of the techniques for efficient inversion of arbitrary covariance matrices arising in least squares estimation. Delosme and Morf have shown how the concept of Toeplitz distance leads to a positive definite embedding via a mixed form representation of the given matrix. In this paper a new method is proposed for the positive definite block-Toeplitz embedding which has the particular feature of taking the signal itself as a starting point. It consists of a suitable cyclic extension and embedding of the given signal in a multichannel stationary signal. The main advantage of the method is that, given the signal, the embedding can be performed by inspection.