A parametrization of the minimal square spectral factors of a nonrational spectral density.
Augusto Ferrante · 1997
Given a nonrational spectral density, minimality for square spectral factors with singularities in both the left and the right half planes is defined. A parametrization of all minimal square spectral factors is then provided in terms of left inner divisors of a certain inner function depending only on the spectral density. Some results on matrix inner functions and minor complements on the Lindquist-Picci stochastic realization theory are also obtained as by-products. Key words: Spectral factor, parametrization, inner function, stochastic realization 1 Introduction The spectral factorization problem, i.e., the problem of finding minimal spectral factors of a matrix-valued spectral density \\Phi(s) is of crucial importance in systems and control theory, circuit theory and prediction theory. In the rational case, parametrizations of minimal stable spectral factors have been obtained starting from the classical results of J. C. Willems [13] on the Algebraic Riccati Equation (ARE), ...