Maximum Ch-entropy estimation of p-adic stationary process and its fast algorithm

In this paper the power spectral density of p-adic stationary stochastic process under the sense of Chrestenson transform (Ch-transform) and its maximum entropy estimator are studied. The relationship formula between the power spectral density and the entropy rate is first derived. The the normal equations of maximum Ch-entropy spectral estimator in closed expression are obtained. When the number of autocorrelation data is p^m, where p⩾2 and m⩾1 are integers, the maximum Ch-entropy estimator can be directly expressed by the known finite autocorrelation data. These results are quite different from that of Fourier´s. Numerical examples are provided to show the effectiveness of the maximum Ch-entropy estimator. General Hadmard ordering is introduced for the Kronecker formulation of the Ch-transform matrix. Such ordering can lead to a fast algorithm proposed in this paper which can reduce the computation complexity front O(p^2m) to O(mp^m) when the number of autocorrelation data is p^m (m>1, p⩾2)