Close frequencies resolution by maximum entropy spectral estimators

We study the properties of the maximum entropy spectral estimator in pure frequencies estimation. We modelize this situation by a sum of pure frequencies added to white noise. We study the effect of the signal to noise ratio and of the autoregressive filter order on the resolution power. Neglecting the uncertainties in the autoregressive filter coefficients estimations we show that the poles of the autoregressive filter transfer function can be classified in two families : one gives the pure frequencies and the other one the white noise. By a first order development we can specify the position of the pure frequencies associated poles. This allows us to give analytical results on the bias of the pure frequency estimation and on the resolution power. These theoretical results are confirmed and illustrated by computer simulations.