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Measure for degree of time variance and measure for degree of non-stationarity: application to discrete LPTV systems
Signal Processing ( IF 4.4 ) Pub Date : 2021-01-19 , DOI: 10.1016/j.sigpro.2021.107995
Ayan Kumar Dutta , Shiv Dutt Joshi , Brejesh Lall

Processing and analysis of time-varying systems and associated non-stationary signals are of great practical importance. The issue of quantifying the amount of time variance and amount of non-stationarity has gained importance recently. This work is also an effort in that direction. In particular, in this paper, we define two measures, one for the degree of time variance (MDTV) in the context of linear periodically time-varying systems (LPTV) and second for the degree of non-stationarity (MDNOST) of cyclostationary processes as they naturally arise when a wide-sense stationary (WSS) process passes through an LPTV system. While MDTV is a system property, on the other hand, MDNOST is a signal property. This paper also tries to find a relationship between the amount of time variation of a system with the amount of non-stationarity it generates. In this light, two concepts are analyzed for two different scenarios. First, we consider a system consisting of an upsampler followed by a linear time-invariant (LTI) filter and second a dual rate system (DRS). Both these systems are LPTV. We have shown that the MDTV generated by both LPTV systems is the same as the MDNOST of their output process through simulations and rigorous mathematical proofs.



中文翻译:

测量时间变化程度和非平稳程度:应用于离散LPTV系统

时变系统和相关的非平稳信号的处理和分析具有非常重要的现实意义。量化时间变化量和非平稳量的问题最近变得越来越重要。这项工作也是朝这个方向的努力。特别是,在本文中,我们定义了两种度量,一种用于时间方差程度(MDTV)在线性周期性时变系统(LPTV)的背景下,其次为非平稳性(MDNOST)是平稳平稳(WSS)过程通过LPTV系统时自然产生的循环平稳过程。而MDTV 另一方面,是系统属性 MDNOST是信号属性。本文还试图找到系统时间变化量与系统产生的非平稳量之间的关系。有鉴于此,针对两个不同的场景分析了两个概念。首先,我们考虑一个系统,该系统由一个上采样器,一个线性时不变(LTI)滤波器和一个双速率系统(DRS)组成。这两个系统都是LPTV。我们已经证明MDTV 两种LPTV系统产生的信号与 MDNOST 通过模拟和严格的数学证明来确定其输出过程。

更新日期:2021-01-24
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