Calculating the Spectral Entropy of a Stationary Random Process

The problem of calculating the spectral entropy of a stationary random process is solved. The spectral entropy (σ-entropy) of a signal is understood as a scalar value characterizing the noise color; it describes the class of signals affecting a system depending on the band under study. By assumption, the random process is defined by a shaping filter, with the Gaussian white noise with a unit covariance matrix supplied at its input, or by an autocorrelation function. The spectral entropy of the stationary random process is analytically derived using a known mathematical model of the shaping filter in the form of a log-determinant function that depends on the transfer matrix and the observability Gramian of the filter. An algorithm for calculating the σ-entropy of stationary random processes with a known autocorrelation function is proposed. The method reduces to reconstructing the mathematical model of the shaping filter using its spectral density factorization. A numerical example is provided: spectral entropy is calculated for a disturbance describing the velocity of wind gusts that affect an aircraft.

spectral entropy, stationary random process, spectral density, autocorrelation function, shaping filter