Authors: Seenu Reddi
Comments: 7 Pages.
Caratheodory's theorem about semi-definite Toeplitz matrices states that for a semi-definite Toeplitz matrix with a unique eigenvalue of zero, the polynomial formed from the elements of the null eigenvector will have zeros on the unit circle. This fact has often been used in spectral analysis to characterize covariance matrices in signal processing and deduce spectrality underlying a given time series. We show that it is possible to form two semi-definite Toeplitz matrices with the kind of property Caratheodory suggests and caution that a careful analysis should be performed before reaching conclusions on the spectrality of the underlying covariance matrix. Numerical examples are presented to illustrate the concepts.
Category: Digital Signal Processing