Properties of the Evolutionary Maximum Entropy Spectral Estimator

2. EVOLUTIONARY MAXIMUM ENTROPY ESTIMATION Using maximum entropy spectral analysis and the theThe Wold-Cramer representation [4] of a non-stationary by considering it the output of a linear timevarying system (LTV) with white noise as input: ory of the Wold-Cramer evolutionary spectrum we develop signal is the evolutionary maximum entropy @ME) estimator for non-stationary signals. The EME estimation reduces to the fitting of a time-varying autoregressive model to the Fourier coefficients of the evolutionary spectrum. The model parameters are efficientlv found bv means of the Levinson alH(n, w)ejwndZ(w) (1) gorithm. Just as in the stationary case, the EME estimator provides very good frequency resolution and can be used to obtain autoregressive models. In this paper, we present the EME estimator and discuss some of its properties. Our aim is to show that the EME estimator has analogous properties to the classical ME estimator for stationary signals.