Stationary Stochastic Signals Research Articles

Denoising With Inherent Scattering Characteristic for 2-D Radar Cross Section Measurement

Noises from the measurement sensors are inevitable in radar cross section testing due to the thermal agitation of electrons in imperfect conductors. Existing methods represented by wavelet threshold usually regard the measured data as a stationary stochastic signal, ignoring the inherent influence of the target under test, which inevitably removes the signal’s component when noise increases. This paper proposes a novel perspective on 2-D radar cross section measurement denoising, considering the target’s inherent scattering characteristics (ISC). In the proposed method, the noise and the target are firstly separated as far as possible in the generalized Fourier series domain while the target’s component is all preserved. Then, the noise is further suppressed by the scattered field reconstruction of the Hankel function. Finally, a metal sphere being a calibrator is introduced to improve the denoising ability. Both simulations and experimental studies demonstrate the superiority of our method compared with existing algorithms. Results indicate that the proposed method can achieve higher accuracy.

Spectral Representation of Stationary and Non-Stationary Stochastic Signals in the Basis of Trigonometric Functions

Spectral Representation of Stationary and Non-Stationary Stochastic Signals in the Basis of Trigonometric Functions

Assessing the detectability of a stochastic gravitational wave background with LISA, using an excess of power approach

The laser interferometer space antenna will be the first gravitational wave observatory in space. It is scheduled to fly in the early 2030’s. LISA design predicts sensitivity levels that potentially enable the detection a stochastic gravitational wave background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.

Jittered Sampling in Linear Canonical Domain

Linear canonical transform (LCT) based sampling has been attracted much attention in signal processing community. A variety of sampling theorems associated with the LCT are therefore derived. However, the random jittered sampling in linear canonical domain still remains unresolved. Starting from the Shannon's result for the LCT, a biased interpolated estimate for bandlimited signals in linear canonical domain from jittered samples is proposed. The inverse filter technique is then applied to correct the bias, giving rise to an unbiased estimator whose interpolation noise variance approaches zero as the jitter becomes less and less pronounced. To be specific, for bandlimited stationary stochastic signals in linear canonical domain the interpolation noise variance is increased, and this result is also verified through some examples and simulations.

Using the Fourier Transform in the Analysis of Vibration Load Tests of Heterogeneous Mechanical Systems

The aim of this study was to find possibilities of using the Fourier transform in the analysis of vibration load tests of heterogeneous mechanical systems, especially those of a biological nature. The study applied the idea that the dispersion of a stationary stochastic signal depends on its power spectral density. We have verified that a sophisticated reduction in the spectral power of the ergodic signal may be used to filter it effectively. The proposed procedure is suitable for the detection and separation of harmonic artefacts. We have created an algorithm in the MATLAB environment and tested its functionality when analysing the vibration transfer within the human axial system.

Performance limitations for LTI discrete-time systems in the presence of stochastic disturbance

ABSTRACTThis paper concerns the fundamental limitations of disturbance rejection for linear time-invariant discrete-time systems under the assumption that the sensor noise is ignorable. The environmental disturbance is modelled as a linear combination of a step signal, a stationary stochastic signal and several sinusoidal signals with different frequencies. Disturbance rejection is measured by the steady-state variance of the residual input of the plant. In studying this problem, it is shown that for minimum phase systems, perfect disturbance rejection can be achieved by minimising the closed-loop sensitivity function. Unlike the minimum phase systems, the performance limitations for non-minimum phase systems are lower bounded by its non-minimum phase zeros, unstable poles and characteristic quantities of the disturbance, where the typical and integral-type control are respectively addressed. Numerical examples are provided to illustrate the utility of the results by analysing the achievable performance.

Bandwidth Estimation From Multiple Level-Crossings of Stochastic Signals

Motivated by a broad range of potential applications in event-driven signal processing inference, we examine a class of spectral moments estimators derived from multiple level-crossings of a stationary Gaussian stochastic signal as well as non-Gaussian signals being monotone transformations of the Gaussian signal. The established spectral moments estimators are used to obtain estimates of the stochastic signal bandwidth. Both the mean-squared bandwidth and the absolute bandwidth are taken into account. Also the notion of the power bandwidth is introduced and its estimation is examined. We prove that the proposed estimates are consistent as the length of the observed time interval is increasing. The accuracy of the proposed bandwidth estimation methods from multiple level-crossings is assessed in simulation studies.

A Multidimensional Cascade Neuro-Fuzzy System with Neuron Pool Optimization in Each Cascade

A new architecture and learning algorithms for the multidimensional hybrid cascade neural network with neuron pool optimization in each cascade are proposed in this paper. The proposed system differs from the well-known cascade systems in its capability to process multidimensional time series in an online mode, which makes it possible to process non- stationary stochastic and chaotic signals with the required accuracy. Compared to conventional analogs, the proposed system provides computational simplicity and possesses both tracking and filtering capabilities.

The effect of dead time on randomly sampled power spectral estimates

We investigate power spectra of a randomly sampled stationary stochastic signal, e.g. a spatial component of a turbulent velocity. We extend the methods of previous authors that basically assumed point or delta function sampling by including features characteristic of real measurement systems. We consider both the effect on the measured spectrum of a finite sampling time, i.e., a finite time during which the signal is acquired, and a finite dead time, that is a time in which the signal processor is busy evaluating a data point and therefore unable to measure a subsequent data point arriving within the dead time delay.

Frequency-Domain Correlation: An Asymptotically Optimum Approximation of Quadratic Likelihood Ratio Detectors

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.

Design of RLS fixed-lag smoother using covariance information in linear discrete stochastic systems

This paper newly designs the recursive least-squares fixed-lag smoother using the covariance information in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The fixed-lag smoother uses the covariance function of the signal in the semi-degenerate kernel form and the variance of the observation noise. The proposed fixed-lag smoother is suitable for the estimations of stationary or non-stationary stochastic signals generally.

Multifractal detrended fluctuation analysis of analog random multiplicative processes

We investigate non-Gaussian statistical properties of stationary stochastic signals generated by an analog circuit that simulates a random multiplicative process with weak additive noise. The random noises are originated by thermal shot noise and avalanche processes, while the multiplicative process is generated by a fully analog circuit. The resulting signal describes stochastic time series of current interest in several areas such as turbulence, finance, biology and environment, which exhibit power-law distributions. Specifically, we study the correlation properties of the signal by employing a detrended fluctuation analysis and explore its multifractal nature. The singularity spectrum is obtained and analyzed as a function of the control circuit parameter that tunes the asymptotic power-law form of the probability distribution function.

Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems

Abstract. This article describes a polynomial estimation technique based on the state‐space model and develops an estimation method for the quadratic estimation problem by applying the multivariate recursive least squares (RLS) Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete‐time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The augmented signal vector is modelled in terms of an autoregressive model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is found to be considerably improved in comparison with the existing RLS Wiener estimators. The proposed method may be applied advantageously to the quadratic estimations of wide‐sense stationary stochastic signals in general.

Design of Quadratic Estimators using Covariance Information in Linear Discrete-Time Stochastic Systems

This paper, apart from the polynomial estimation technique based on the state-space model, examines to develop an estimation method for the quadratic estimation problem by applying the multivariate RLS Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete-time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The signal vector is modeled in terms of an AR model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is fairly improved in comparison with the existing RLS Wiener estimators. It is advantageous that the proposed method can be applied to the quadratic estimations of wide-sense stationary stochastic signals in general.

RLS fixed-lag smoother using covariance information in linear continuous stochastic systems

This paper newly designs the recursive least-squares fixed-lag smoother using the covariance information in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The fixed-lag smoother uses the covariance function of the signal in the semi-degenerate kernel form and the variance of the observation noise. The proposed fixed-lag smoother is appropriate for the estimations of stationary or non-stationary stochastic signals generally.

Transfer Functions and Statistical Analysis of FDLCP Systems Described by Higher-order Differential Equations

The paper considers the investigation of finitedimensional linear continuous-time periodic (FDLCP) systems, where the process is described by differential equations of higher than first order, and is influenced by a differentiated input signal. The concept of quasistationary motion mode for such systems is introduced, and closed formulae are derived for calculating statistical characteristics of the quasi-stationary output, when the process is excited by a stationary stochastic signal. Moreover, closed formulae for determining the H2- norm and associated H∞-norms are derived. The methods use a generalization of the parametric transfer matrix (PTM) concept for FDLCP systems of the considered class, and then apply the corresponding classical frequency-domain methods for statistical analysis of continuous-time LTI systems.

Statistical analysis of stable FDLCP systems by parametric transfer matrices

This paper considers the problem of determining the statistical characteristics of the response of internally stable finite-dimensional continuous-time periodic (FDLCP) systems to stationary stochastic input signals. Closed formulae for calculating the variance matrix of the state and the output vectors are derived, as well as for the mean variance of the output and the 2-norm of the systems, where only matrices of finite dimension are used. The method bases on application of the parametric transfer matrix (PTM) and needs a precalculation of the transition matrix of the system on the interval 0≤ t ≤ T, where T is the period of the system.

A periodogram-based test method for comparing stationary stochastic signals

A periodogram-based test method for comparing stationary stochastic signals

Neural filtering method for stationary signal processes

In this paper a new method of neural filtering using artificial neural network systems is presented for the filtering problems of linear and nonlinear, stationary and nonstationary stochastic signals. The neural filter (denoted neurofilter) developed in this paper has either finite impulse response (FIR) structure or infinite impulse response (IIR) structure. The neurofilter differs from the conventional linear digital FIR and IIR filters because the artificial neural network system used in the neurofilter has a nonlinear structure due to the sigmoid function. Numerical studies for the estimation of a second-order Butterworth process are performed by changing the structures of the neurofilter in order to evaluate the performance indices under changes of the output noises or disturbances. The results obtained from these studies verified the capabilities which are essentially necessary for on-line filtering of various stochastic signals.

Estimation technique using covariance information with uncertain observations in linear discrete-time systems

This paper proposes the recursive estimation technique using the covariance information in linear stationary discrete-time systems when the uncertain observations are given. At first, recursive least-squares algorithms for the filtering, fixed-point smoothing and one-step ahead prediction estimates are designed. The estimators use the crossvariance function of the state variable, that generates the signal process, with the signal, the observation vector, the system matrix, the variance of white Gaussian observation noise, the observed value and the probability that the signal exists in the uncertain observation. Second, to obtain the necessary information related to the covariance function of the signal in the estimators, we show the factorization method for the observation vector, the crossvariance function and the system matrix from the autocovariance function of the signal. As a result, the proposed technique uses finite number of autocovariance data of the stationary stochastic signal, the variance of white Gaussian observation noise, the uncertain observations and the probability.