An Investigation on Maximum Entropy Estimation Based on Chrestenson Transform

Abstract

In this paper, we re-visit the topics of maximum entropy estimation in the sense of Chrestenson transform. As we all well know, maximum entropy estimation in the sense of Fourier’s transform was well investigated and well-known Levinson-Burg algorithm was proposed and is widely used. We first elucidated the maximum entropy estimation based on [2], and then based on [2] derived and indicated the conditions where entropy rate h, as defined in the paper, converges and exists. Finally, we derive a general maximum entropy estimation for Chrestenson transform, and it shows that Levinson-Burg algorithm still applies in the sense of Chrestenson Transform. We also show that when the sampling data is p, an actual and complete spectral estimation can be obtained by a fast algorithm which is in line with part results in [2].