non-Gaussian Analysis Research Articles

Evaluation of beat noise in OCDMA system with non-Gaussian approximated method

With the development of phase encoding technologies, beat noise becomes one of the most predominant limitations of optical code division multiaccess (OCDMA) systems. In order to analyze beat noises' impact more accurately, a non-Gaussian analysis with consideration of a decision variable's moment generation function is first introduced in this paper to evaluate both the multiaccess interference and the beat noises simultaneously, where prime, secondary, and partial coherent beat noises are discussed in detail. In this paper, the saddle-point approximation (SPA) method is first utilized to investigate beat noise's impact on an OCDMA system. Comparison of probability density functions as well as bit error rates between the proposed method and the traditional Gaussian approximation method is given here. The resultant achievement shows the outstanding performance of SPA on this occasion, which proves the necessity of such a moment generation function-based non-Gaussian analysis

Analysis of Diffusion Constant and Non-Gaussianity near the Glass Transition Point in the Frequency Domain

A novel method is developed for estimating the diffusion constant D c and the non-Gaussian parameter A ( t ) on the basis of measurement in the frequency region. This method is shown to have merits over the conventional one in which a limited time window is used. To confirm the validity of this method, it is applied to a binary soft-sphere fluid which was studied by molecular dynamics (MD) simulation. The diffusion constant D c is determined in the region closer to the glass transition than in the conventional MD simulation. The temperature dependence of the exponent of A ( t ) is consistent with that predicted by the trapping diffusion model.

Prospects for ACT: Simulations, power spectrum, and non-Gaussian analysis

A new generation of instruments will reveal the microwave sky at high resolution. We focus on one of these, the Atacama Cosmology Telescope, which probes scales 1000<l<10,000, where both primary and secondary anisotropies are important. Including gravitational lensing, thermal and kinetic Sunyaev–Zeldovich (SZ) effects, and extragalactic point sources, we simulate the telescope’s observations of the CMB in three channels, then extract the power spectra of these components in a multifrequency analysis. We present results for various cases, differing in assumed knowledge of the contaminating point sources. We find that both radio and infrared point sources are important, but can be effectively eliminated from the power spectrum given three (or more) channels and a good understanding of their frequency dependence. However, improper treatment of the scatter in the point source frequency dependence relation may introduce a large systematic bias. Even if all thermal SZ and point source effects are eliminated, the kinetic SZ effect remains and corrupts measurements of the primordial slope and amplitude on small scales. We discuss the non-Gaussianity of the one-point probability distribution function as a way to constrain the kinetic SZ effect, and we develop a method for distinguishing this effect from the CMB in a window where they overlap. This method provides an independent constraint on the variance of the CMB in that window and is complementary to the power spectrum analysis.

Investigations on Non-Gaussian Factor Analysis

This letter further explores the Bayesian Ying-Yang learning based non-Gaussian factor analysis (NFA) via investigating its key yet analytically intractable factor estimating step. Among the three suggested numerical approaches we empirically show that the so-called iterative fixed posteriori approximation approach is the most optimal, as well as theoretically prove that the iterative fixed posteriori approximation is another type of EM-algorithm, with the proof of its convergence also shown.

On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ in the model one-dimensional case. The main results are a detailed intrinsic description of spaces of test functions, a description of generalized translation operators, and the investigation of integral C- and S-transformations.

Pseudodifferential equations and a generalized translation operator in non-gaussian infinite-dimensional analysis

Pseudodifferential equations of the formv(Dx)y=f (here,v is a function holomorphic at zero andD x is a pseudodifferential operator) are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to the construction of a generalized translation operatorT y χ =χ( ) on the spaces indicated and to the investigation of its properties. In particular, we prove the associativity, commutativity, and other properties ofT y χ , which are analogs of the classical properties of a generalized translation operator.

Non-Gaussian along-wind response analysis in time and frequency domains

With special reference to the role of the non-Gaussian nature of the response, the procedures for along-wind frequency-domain analysis of MDOF structures are discussed. Assuming turbulence as a homogeneous Gaussian field, the dynamic response of structural systems is evaluated by using the power spectral density of the wind force in the case of the standard Gaussian analysis and by using both the power spectral density and bi-spectrum in the case of non-Gaussian analysis. The statistics of the response is used to estimate the peak value distribution. A parametric analysis, carried out on a steel lattice broadcasting antenna, and the comparison with suited time domain analyses of the response allowed to evaluate the reliability of the spectral methods.

Searching for non-gaussianity: Statistical tests

Non-gaussianity represents the statistical signature of physical processes such as turbulence. It can also be used as a powerful tool to discriminate between competing cosmological scenarios. A canonical analysis of non-gaussianity is based on the study of the distribution of the signal in the real (or direct) space (e.g. brightness, temperature). This work presents an image processing method in which we propose statistical tests to indicate and quantify the non-Gaussian nature of a signal. Our method is based on a wavelet analysis of a signal. Because the temperature or brightness distribution is a rather weak discriminator, the search for the statistical signature of non-gaussianity relies on the study of the coefficient distribution of an image in the wavelet decomposition basis which is much more sensitive. We develop two statistical tests for non-gaussianity. In order to test their reliability, we apply them to sets of test maps representing a combination of Gaussian and non-Gaussian signals. We deliberately choose a signal with a weak non-Gaussian signature and we find that such a non-Gaussian signature is easily detected using our statistical discriminators. In a second paper, we apply the tests in a cosmological context.

Generalized functions in infinite-dimensional analysis

We give a general approach to infinite dimensional non-Gaussian Analysis which generalizes the work [ADKS94] to measures which possess more singular logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.

A generalization of white noise analysis by means of theory of hypergroups

A wide generalization of the construction of non-Gaussian analysis in the one-dimensional case is proposed in which instead of the exponentials the characters of commutative hypergroup are used.

Infinite-dimensional non-gaussian analysis and generalized translation operators

Infinite-dimensional non-gaussian analysis and generalized translation operators

Non-Gaussian analysis and hypergroups

UDC 517.515 In recent years two approaches to the generalization of the Gaussian infinite-dimensional analysis (white noise analysis) to non-Gaussian measures have appeared: one of them is based on spectral theory for families of commuting self-adjoint operators [1, 2] and the other proceeds from biorthogonal expansions [3, 4]. In this note we show that in the one-dimensional model case the second approach can be extensively generalized if the characters of an Ll-hypergroup are used in its construction instead of exponential functions. For the properties of hypergroups applied below see [5-7] (here we use the term "Ll-hypergroup" instead of "hypercomplex system with locally compact base" according to [7]). 1. Consider a commutative Ll-hypergroup H I with locally compact basis Q, nonnegative structure measure, and multiplicative measure din(x) (x e Q); H I is assumed to be normal (Q 9 x ~-~ x* • Q is

Treatment of gross errors using maximum probability theory

We describe a nonlinear analysis scheme capable of directly treating observations which have a non-Gaussian error distribution. This non-Gaussian analysis scheme is shown to be a generalization of the familiar optimum interpolation scheme and must be solved iteratively. the approach to the treatment of gross errors is compared with a more traditional approach in which a quality-control step precedes the analysis. Simulation experiments are performed in which the observations have many of the characteristics of observations from the proposed space-borne atmospheric laser Doppler instrument and a 50% probability of gross error. Both approaches are shown to perform well, with the non-Gaussian analysis giving the better results.

Extension of an Itô-based general approximation technique for random vibration of a BBW general hysteris model part II: Non-Gaussian analysis

The work presented in this paper constitutes the second phase of on-going research aimed at developing mathematical models for representing general hysteretic behavior of structures and approximation techniques for the computation and analysis of the response of hysteretic systems to random excitations. In this second part, the technique previously developed by the authors for the Gaussian response analysis of non-linear systems with general hysteretic behavior is extended for the non-Gaussian analysis of these systems. This approximation technique is based on the approach proposed independently by Ibrahim and Wu-Lin. In this work up to fourth order moments of the response co-ordinates are obtained for the Bouc-Baber-Wen smooth hysteresis model. These higher order statistics previously have not been made available for general hysteresis models by using existing approximation methods. Second order moments obtained for the model by this non-Gaussian closure scheme are compared with equivalent linearization and Gaussian closure results via Monte Carlo simulation (MCS). Higher order moments are compared with the simulation results. The study performed for a wide range of degradation parameters and input power spectral density ( PSD) levels shows that the non-Gaussian responses obtained by this approach are in better agreement with the MCS results than the linearized and Gaussian ones. This approximation technique can provide information on higher order moments for general hysteretic systems. This information is valuable in random vibration and the reliability analysis of hysteretically yielding structures.

Deconvolution as a feasible alternative to the root-sum-squares rule for non-Gaussian transition duration analysis

A 100-ps Debye line filter is analyzed for transition duration using both deconvolution and root-sum-squares methods. The latter method shows errors of ±12 percent for the cases presented, while deconvolution agrees to within 0.3 percent of the theoretical filter model. In addition, the deconvoluted Debye filter waveform matches the theoretical step response to within less than 1 percent at all points in a 500-ps time epoch.