NORMS OF POSITIVE DEFINITE TOEPLITZ MATRICES AND DETECTION OF ALMOST PERIODIC COMPONENTS IN RANDOM SIGNALS

VADYM ADAMYAN, J.L. Iserte Vilar, Tkachenko Gorski Igor Mijail, Verdú Martín Gumersindo Jesús

2014

Operators and Matrices

For positive definite Toeplitz matrices generated by trigonometric moments of a non-negative measure we note that the Hilbert-Schmidt norm and the maximal eigenvalue satisfy certain limiting relations. Analogous relations hold for positive definite integral operators with difference kernels. The obtained relations are used in order to detect hidden almost periodic components in random signals.