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AN OVERVIEW OF FRACTIONAL ORDER SIGNAL PROCESSING (FOSP) TECHNIQUES

机译:分数阶信号处理(FOSP)技术概述

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摘要

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 (ARFDVIA); 3) 1/f~α noise; 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.
机译:本文简要介绍了一些现有的分数阶信号处理(FOSP)技术,其中介绍了数学界的发展。证明了分数运算符与远程依赖关系,并总结了每种技术的基本性质及其一些应用。具体来说,我们提供了一个关于1)分数阶线性系统的教程; 2)自回归分数积分移动平均值(ARFDVIA); 3)1 / f〜α噪声; 4)赫斯特参数估计; 5)分数阶傅立叶变换(FrFT); 6)分数阶线性变换(Hartley,Sine,Cosine); 7)分形; 8)分数阶样条; 9)分数低阶矩(FLOM)和10)分数延迟滤波器。只要有可能,我们都会指出这些FOSP技术之间的联系。

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