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

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