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

Abstract

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/sup m/, where p/spl ges/2 and m/spl ges/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/sup 2m/) to O(mp/sup m/) when the number of autocorrelation data is p/sup m/ (m>1, p/spl ges/2).<>