An Overview of Fractional Order Signal Processing (FOSP) Techniques

Abstract

This paper presents a brief overview of some existing fractional order signal processing (FOSP) techniques where the developments in the mathematical communities are introduced; relationship between the fractional operator and long-range dependence is demonstrated, and fundamental properties of each technique and some of its applications are summarized. Specifically, we presented a tutorial on 1) fractional order linear systems; 2) autoregressive fractional integrated moving average (ARFIMA); 3) 1/fαnoise; 4) Hurst parameter estimation; 5) fractional order Fourier transformation (FrFT); 6) fractional order linear transforms (Hartley, Sine, Cosine); 7) fractal; 8) fractional order splines; 9) fractional lower order moments (FLOM) and 10) fractional delay filter. Whenever possible, we indicate the connections between these FOSP techniques.