Spectrum Estimation and System Identification

This detailed study of spectrum estimation and system identification emphasizes a new approach that makes use of the nonnegativity condition of the spectrum. Beginning with second-order stationary stochastic processes, the one-to-one relationship between their spectra and bounded (or positive) functions is used to exhibit all solutions to the classical trigometric moment problem that deals with the extension of the given partial set of autocorrelations. A new approach that exploits rationality is presented for identifying the model order and system parameters of ARMA (rational) systems from their output measurements. This approach also provides rational approximations of nonrational systems. Extensions to the multichannel case in all of the above situations are also analyzed.