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A New Concept of Fractional Order Cumulant and It-Based Signal Processing in alpha and/or Gaussian Noise

Shi, Y, Yu, DL, Shi, H and Shi, Y (2020) A New Concept of Fractional Order Cumulant and It-Based Signal Processing in alpha and/or Gaussian Noise. IEEE Transactions on Information Theory, 67 (3). pp. 1849-1863. ISSN 0018-9448

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Abstract

In this article, the concept and definitions of the Fractional Order Moment (FOM) and Fractional Order Cumulant (FOC) are proposed, which is based on the fractional derivative of the fractional order Moment-generating function and the fractional order Cumulant-generating function of stochastic processes. The moment and cumulant are defined on an expanded set from positive integer to the whole positive real. This development not only provides a new technology for signal processing, also complements the existing theory in the field. The properties of the FOC have been derived, and their uniformity and particularity with the High Order Cumulant are compared and commented. In addition, the transformation between the FOM and the FOC are derived and discussed in detail. As one of the applications of the new concept to the α and Gaussian processes, a new method of suppressing α and Gaussian noise is proposed. Furthermore, a FOC-based parameter estimation algorithm is developed for the non-minimum phase ARMA processes in α and/or Gaussian noise. Simulation examples are used to demonstrate the effectiveness of the proposed parameter estimation algorithm.

Item Type: Article
Additional Information: © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Uncontrolled Keywords: 0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Engineering
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Related URLs:
Date Deposited: 25 Mar 2021 09:51
Last Modified: 25 Mar 2021 10:00
DOI or Identification number: 10.1109/TIT.2020.3042347
URI: https://researchonline.ljmu.ac.uk/id/eprint/14669

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