Radiometric Identification of Signals by Matched Whitening Transform

Radiometric identification is the problem of attributing a signal to a specific source. In this work, a radiometric identification algorithm is developed using the whitening transformation. The approach stands out from the more established methods in that it works directly on the raw IQ data and hence is featureless. As such, the commonly used dimensionality reduction algorithms do not apply. The premise of the idea is that a data set is “most white” when projected on its own whitening matrix than on any other. In practice, transformed data are never strictly white since the training and the test data differ. The Förstner-Moonen measure that quantifies the similarity of covariance matrices is used to establish the degree of whiteness. The whitening transform that produces a data set with the minimum Förstner-Moonen distance to a white noise process is the source signal. The source is determined by the output of the mode function operated on the Majority Vote Classifier decisions. Using the Förstner-Moonen measure presents a different perspective compared to maximum likelihood and Euclidean distance metrics. The whitening transform is also contrasted with the more recent deep learning approaches that are still dependent on feature vectors with large dimensions and lengthy training phases. It is shown that the proposed method is simpler to implement, requires no features vectors, needs minimal training and because of its non-iterative structure is faster than existing approaches.

SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.

Phase Congruential White Noise Generator

White noise generators can use uniform random sequences as a basis. However, such a technology may lead to deficient results if the original sequences have insufficient uniformity or omissions of random variables. This article offers a new approach for creating a phase signal generator with an improved matrix of autocorrelation coefficients. As a result, the generated signals of the white noise process have absolutely uniform intensities at the eigen Fourier frequencies. The simulation results confirm that the received signals have an adequate approximation of uniform white noise.

Statistics of an Appealing Class of Random Processes

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

Linear Stochastic Models in Discrete and Continuous Time

The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [0,π] radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.

DYNAMIC BEHAVIOR OF TWO ELASTICALLY CONNECTED NANOBEAMS UNDER A WHITE NOISE PROCESS

This paper investigates the almost-sure and moment stability of a double nanobeam system under stochastic compressive axial loading. By means of the Lyapunov exponent and the moment Lyapunov exponent method the stochastic stability of the nano system is analyzed for different system parameters under an axial load modeled as a wideband white noise process. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises.

Quantum Decomposition Associated with the q-Deformed Lévy–Meixner White Noise

In this paper we start with a new detailed construction of the one-mode type q-Lévy-Meixner Fock space [Formula: see text] which serves to obtain the quantum decomposition associated with the q-deformed Lévy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-Lévy-Meixner white noise [Formula: see text], we study the chaos property of the noncommutative L2-space with respect to the vacuum expectation τ. Next, we determine the distribution of the q-Lévy-Meixner operator J(χD) = ⟨ω, χD⟩ and as a consequence we give some useful properties of the q-Lévy-Meixner white noise process.

A condition-based preventive replacement policy with imperfect manual inspection for a two-stage deterioration process

This article proposes a novel preventive replacement policy based on condition monitoring and imperfect manual inspection for systems subject to a two-stage deterioration process, where the two-stage deterioration process is modeled by the white noise process and Brownian motion with a drift, respectively. The proposed preventive replacement policy is implemented using two thresholds: a failure threshold and a preventive threshold. Specifically, if the condition monitoring measurement is observed to cross the failure threshold, then the failure replacement will be carried out; and, if the condition monitoring measurement is observed to cross the preventive threshold while lower than the failure threshold, then the system needs to be checked by manual inspection, and the preventive replacement will be carried out once the system is found to be in the defective state. In this article, we consider that manual inspection is imperfect, namely, there is a probability that the defect will be unnoticed. By minimizing the expected cost per unit time, we obtain the optimal condition monitoring interval and preventive threshold. A numerical example is provided to demonstrate the performance of the proposed condition-based replacement policy. Comparisons are made with the existing work, which shows the effectiveness and superiority of the proposed policy.

Empirical White Noise Processes and the Subjective Probabilistic Approaches

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

ABSTRACTFrom observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an analytical framework that allows determination of the probability density function (PDF) for a stochastic process beyond fractional Brownian motion. Using passive microrheology via videomicroscopy, mean square displacements (MSD) of tracer particles suspended in fibrin at different ageing times are obtained. The anomalous diffusion is then described by a damped white noise process with memory, with analytical results closely matching experimental plots of MSD and PDF. We further show that the white noise functional stochastic approach applied to passive microrheology reveals the existence of a gelation parameterμwhich elucidates the dynamics of constrained tracer particles embedded in a time dependent soft material. This study offers experimental insights on the ageing of fibrin gels while presenting a white noise functional stochastic approach that could be applied to other systems exhibiting non-Markovian diffusive behavior.