Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. In this paper we provide a joint framework for all three representations in the context of frequency-domain stochastic modeling. This framework allows us to extend many established statistical procedures for bivariate vector time series to complex-valued and rotary representations. These include procedures for parametrically modeling signal coherence, estimating model parameters using the Whittle likelihood, performing semi-parametric modeling, and choosing between classes of nested models using model choice. We also provide a new method of testing for impropriety in complex-valued signals, which tests for noncircular or anisotropic second-order statistical structure when the signal is represented in the complex plane. Finally, we demonstrate the usefulness of our methodology in capturing the anisotropic structure of signals observed from fluid dynamic simulations of turbulence.Comment: To appear in IEEE Transactions on Signal Processin

Method of spectral analysis of traction current of AC electric locomotives

An improved method for spectral analysis of traction current of an Alternating Current (AC) electric locomotive is considered in the article. A new method of spectral analysis considers the change in voltage in the catenary system as a non-deterministic, non-ergodic and non-Gaussian process. It has been established that higher voltage harmonics in the catenary system have a significant negative effect on the operation of non-traction railway consumers of electricity. In addition, electric locomotives operating in the same feeder zone have a mutual influence on each other. Electric railway transport is a source of higher voltage harmonics and strongly distorts the shape of the sinusoidal voltage of the catenary system, which are caused by the higher spectral components of the current in the electric locomotive traction drive circuit. These spectral components of the traction current arise in the traction drive circuit due to the nonlinearity of the current-voltage characteristics of the electronic devices of an electric locomotive, for example, a contact rectifier, a capacitor circuit of traction motors. Reactive power compensators are used in electric locomotives to eliminate components of higher harmonic traction current in the catenary system. Traditionally, spectral analysis in such systems is performed using Fourier methods. However, the determination of the spectral components of the traction current by the Fourier method for constructing a control system for a reactive power compensator is possible only if the process of voltage variation is a deterministic or ergodic Gaussian process. Otherwise, the application of Fourier transform methods will be incorrect. An analysis of the factors that affect voltage changes in the catenary system showed that this process is significantly different from the ergodic Gaussian process. Such factors include the following: the operating mode of the electric locomotives; number and total capacity of electric locomotives in one feeder zone; electric locomotives passing through feeder zones; instability of collection current. Thus, in the case under consideration, the application of the Fourier methods is incorrect for the analysis of the spectral components of the traction current. This affects the quality of compensation of the higher harmonic components of the traction current, and in some cases, the unstable operation of the control system of the active part of the reactive power compensator. Proposed scientific approach is based on the Levinson–Durbin linear prediction algorithm. On the one hand, this allows adapting the control system of the compensator to the voltage parameters of the catenary system. On the other hand, this allows taking into account the operating modes of electric rail vehicle with reactive power compensation. The construction of a compensator control system using the Levinson–Durbin algorithm significantly simplifies thensynchronization scheme of the compensator and power circuits of the traction electric drive of AC electric locomotive. A comparison of the traditional method of spectral analysis, based on the Fast Fourier Transform (FFT), and the method, based on the Levinson–Durbin algorithm, proposed by the authors, showed the high efficiency of the latter. First published online 21 January 202

A Widely Linear Complex Autoregressive Process of Order One

We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This process can then capture elliptical, as opposed to circular, stochastic oscillations in a bivariate signal. The process is order one and is more parsimonious than alternative stochastic modeling approaches in the literature. We provide conditions for stationarity, and derive the form of the covariance and relation sequence of this model. We describe how parameter estimation can be efficiently performed both in the time and frequency domain. We demonstrate the practical utility of the process in capturing elliptical oscillations that are naturally present in seismic signals