Showing papers on "White noise published in 1993"
28 Oct 1993
TL;DR: The motivation behind the use of higher-order spectra (HOS) in signal processing as well as the definitions, properties, and biomedica1 signal processing applications of higher order spectra are presented.
Abstract: Absltacl The purpose of this keynote lecture of the Signal Analysis Track is U) present the motivation behind he use of higher-order spectra (HOS) in signal processing as well as the definitions, properties, and biomedica1 signal processing applications of higher-order spectra. This lecture will also emphasize the state of science of the higher-order spectra field, especially as it applies to non-stadonary signal analysis.
378 citations
17 Jan 1993
TL;DR: The author derives exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the normalized logarithmic density (NLD), and shows that the exponent of the random coding bound can be attained by linear ICs (lattices), implying that lattices play the same role with respect to the AWGN channel as linear-codes do with respectto a discrete symmetric channel.
Abstract: Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Euclidean space. The author regards an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding rate is meaningless and the author uses, instead of coding rate, the normalized logarithmic density (NLD). The maximum value C/sub /spl infin// such that, for any NLD less than C/sub /spl infin//, it is possible to construct an PC with arbitrarily small decoding error probability, is called the generalized capacity of the AWGN channel without restrictions. The author derives exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the NLD. The upper bound is obtained by means of a random coding method and it is very similar to the usual random coding bound for the AWGN channel. The exponents of these upper and lower bounds coincide for high values of the NLD, thereby enabling derivation of the generalized capacity of the AWGN channel without restrictions. It is also shown that the exponent of the random coding bound can be attained by linear ICs (lattices), implying that lattices play the same role with respect to the AWGN channel as linear-codes do with respect to a discrete symmetric channel. >
324 citations
TL;DR: The online EM schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes.
Abstract: Sequential or online hidden Markov model (HMM) signal processing schemes are derived, and their performance is illustrated by simulation. The online algorithms are sequential expectation maximization (EM) schemes and are derived by using stochastic approximations to maximize the Kullback-Leibler information measure. The schemes can be implemented either as filters or fixed-lag or sawtooth-lag smoothers. They yield estimates of the HMM parameters including transition probabilities, Markov state levels, and noise variance. In contrast to the offline EM algorithm (Baum-Welch scheme), which uses the fixed-interval forward-backward scheme, the online schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes. Similar techniques are used to derive online schemes for extracting finite-state Markov chains imbedded in a mixture of white Gaussian noise (WGN) and deterministic signals of known functional form with unknown parameters. >
289 citations
TL;DR: One-dimensional traffic flow is simulated by a cellular-automaton-type discrete model, which shows a phase transition between a jam phase and a non-jam phase and by adding random perturbations finds a 1/f power spectrum in the jam phase, whereas a white noise is observed in the non- jam phase.
Abstract: One-dimensional traffic flow is simulated by a cellular-automaton-type discrete model. As we increase the car density, the model shows a phase transition between a jam phase and a non-jam phase. By adding random perturbations we found a 1/f power spectrum in the jam phase, whereas a white noise is observed in the non-jam phase.
272 citations
TL;DR: This paper presents a new approach to generate multidimensional Gaussian random fields over a regular sampling grid that is both exact and computationally very efficient and comparable with that of a spectral method also implemented using the FFT.
Abstract: To generate multidimensional Gaussian random fields over a regular sampling grid, hydrogeologists can call upon essentially two approaches. The first approach covers methods that are exact but computationally expensive, e.g., matrix factorization. The second covers methods that are approximate but that have only modest computational requirements, e.g., the spectral and turning bands methods. In this paper, we present a new approach that is both exact and computationally very efficient. The approach is based on embedding the random field correlation matrix R in a matrix S that has a circulant/block circulant structure. We then construct products of the square root S1/2 with white noise random vectors. Appropriate sub vectors of this product have correlation matrix R, and so are realizations of the desired random field. The only conditions that must be satisfied for the method to be valid are that (1) the mesh of the sampling grid be rectangular, (2) the correlation function be invariant under translation, and (3) the embedding matrix S be nonnegative definite. These conditions are mild and turn out to be satisfied in most practical hydrogeological problems. Implementation of the method requires only knowledge of the desired correlation function. Furthermore, if the sampling grid is a d-dimensional rectangular mesh containing n points in total and the correlation between points on opposite sides of the rectangle is vanishingly small, the computational requirements are only those of a fast Fourier transform (FFT) of a vector of dimension 2dn per realization. Thus the cost of our approach is comparable with that of a spectral method also implemented using the FFT. In summary, the method is simple to understand, easy to implement, and is fast.
243 citations
TL;DR: A quantitative measure of determinism in a recurrent time series is developed using scalar time series data to form a vector series in reconstructed phase space and a statistic is developed to measure the observed «continuity» of the vector series.
Abstract: A quantitative measure of determinism in a recurrent time series is developed. Specifically, scalar time series data are used to form a vector series in reconstructed phase space. A statistic is then developed to measure the observed ``continuity'' of the vector series. The statistic is used as a measure of determinism. Several examples are included to demonstrate the effectiveness of the method.
196 citations
TL;DR: The behavior of least-mean-square (LMS) and normalized least- Mean- square (NLMS) algorithms with spherically invariant random processes (SIRPs) as excitations is shown.
Abstract: The behavior of least-mean-square (LMS) and normalized least-mean-square (NLMS) algorithms with spherically invariant random processes (SIRPs) as excitations is shown. Many random processes fall into this category, and SIRPs closely resemble speech signals. The most pertinent properties of these random processes are summarized. The LMS algorithm is introduced, and the first- and second-order moments of the weight-error vector between the Wiener solution and the estimated solution are shown. The behavior of the NLMS algorithm is obtained, and the first- and second-order moments of the weight-error vector are calculated. The results are verified by comparison with known results when a white noise process and a colored Gaussian process are used as input sequences. Some simulation results for a K/sub 0/-process are then shown. >
146 citations
TL;DR: It is shown that the channel capacity can be achieved by equiprobable signaling with geometrical, Gaussian-like signal sets, and implicates that it is possible to approach channel capacity without using any kind of shaping codes.
Abstract: For the additive white Gaussian noise channel, there is a gap between the channel capacity and the highest achievable rate of equiprobable uniformly spaced one-dimensional signaling. It is commonly believed that approaching channel capacity requires the constituent one-dimensional signal points to have a Gaussian probability distribution. It is shown that the channel capacity can be achieved by equiprobable signaling with geometrical, Gaussian-like signal sets. Construction of these signal constellations is explicitly given. This result implicates that it is possible to approach channel capacity without using any kind of shaping codes. >
143 citations
Book•
12 May 1993
TL;DR: In this paper, Symmetric white noise on Bose Fock space and symmetrization of symmetric white noises have been studied, as well as Quadratic components of conditionally positive linear functionals.
Abstract: Basic concepts and first results.- Symmetric white noise on Bose Fock space.- Symmetrization.- White noise on bose fock space.- Quadratic components of conditionally positive linear functionals.- Limit theorems.
131 citations
TL;DR: Two dynamical systems in R 2 given by an ODE are provided: one which explodes in finite time for every initial condition but becomes stable by adding white noise of arbitrary positive intensity and another which becomes explosive when it is perturbed by additive white noise.
Abstract: We provide two dynamical systems in R 2given by an ODE:One which explodes in finite time for every initial condition but becomes stable by adding white noise of arbitrary positive intensity in the sense that the system becomes nonexplosive and even positive recurrent and another system which is globally asymptotically stable and which becomes explosive when it is perturbed by additive white noise
TL;DR: A numerical simulation technique is presented that combines the advantages of the discrete Fourier transform (DFT) algorithm and a digital filtering scheme to generate continuous long-duration multivariate random processes.
Abstract: A numerical simulation technique is presented that combines the advantages of the discrete Fourier transform (DFT) algorithm and a digital filtering scheme to generate continuous long-duration multivariate random processes. This approach offers the simple convenience of conventional fast Fourier transform (FFT) based simulation schemes; however, it does not suffer from the drawback of the large computer memory requirement that in the past has precluded the generation of long-duration time series utilizing FFT-based approaches. Central to this technique is a simulation of a large number of time series segments by utilizing the FFT algorithm, which are subsequently synthesized by means of a digital filter to provide the desired duration of simulated processes. This approach offers computational efficiency, convenience, and robustness. The computer code based on the present methodology does not require users to have experience in determining optimal model parameters, unlike the procedures based on parametric models. The effectiveness of this methodology is demonstrated by means of examples concerning the simulation of a multivariate random wind field and the spatial variation of wave kinematics in a random sea with prescribed spectral descriptions. The simulated data showed excellent agreement with the target spectral characteristics. The proposed technique has immediate applications to the simulation of real-time processes.
TL;DR: It is proved that any random sequence can be exhibited as the output of a stochastic dynamical system driven by white noise.
Abstract: It is proved that any random sequence can be exhibited as the output of a stochastic dynamical system driven by white noise. Further refinements are obtained for Markov, stationary, and ergodic sequences. This settles some open problems in stochastic realization theory posed by Willems and Van Schuppen [NATO ASI-AMS Seminar on Algebraic and Geometric Methods in Linear System Theory, Harvard University, Cambridge, MA, 1979].
TL;DR: In this article, the phenomenon of stochastic resonance (SR) was investigated for chaotic systems perturbed by white noise and a harmonic force, and it was shown that SR can be realized via both parameter variation (in the absence of noise) and by variation of the noise intensity with fixed values of the other parameters.
Abstract: The phenomenon of stochastic resonance (SR) is investigated for chaotic systems perturbed by white noise and a harmonic force. The bistable discrete map and the Lorenz system are considered as models. It is shown that SR in chaotic systems can be realized via both parameter variation (in the absence of noise) and by variation of the noise intensity with fixed values of the other parameters.
TL;DR: In this paper, a scale of spaces of test functions and associated distributions in white noise analysis is introduced, and a characterization of the spaces considered in terms of analytic and growth properties of the corresponding S-transforms is given.
TL;DR: In this article, the existence of solutions for nonlinear evolution equations with nonhomogenous boundary conditions of white noise type is studied. And it is shown that if the nonlinearity satisfies appropriate dissipativity conditions, then it has a solution as well.
Abstract: The paper is devoted to nonlinear evolution equations with nonhomogenous boundary conditions of white noise type Necessary and sufficient conditions for the existence of solutions in the linear case are given It is also shown that if the nonlinearity satisfies appropriate dissipativity conditions the nonlinear equation has a solution as well The results are applied to equations with polynomial nonlinearities
TL;DR: Using compact closed form formulas for the Cramer Rao Bound corresponding to the joint estimation of the directions-of-arrival, the signal covariance matrix, and the noise variance, it is observed that under certain conditions, correlation phase has a strong effect on DOA estimation accuracy.
Abstract: In this paper we present compact closed form formulas for the Cramer Rao Bound corresponding to the joint estimation of the directions-of-arrival, the signal covariance matrix, and the noise variance. Using these formulas we investigate the effect of signal correlation on the achievable accuracy of direction finding system in a correlated signal environment. As expected, estimation accuracy decreases with increasing correlation magnitude. We observe that under certain conditions (small aperture, high correlation magnitude), correlation phase has a strong effect on DOA estimation accuracy.
TL;DR: The authors examine maximum-likelihood block detection of uncoded full response continuous phase modulation over an additive white Gaussian noise (AWGN) channel and finds many new receiver structures that can be compared to the traditional ones that have been used in the past.
Abstract: The authors examine maximum-likelihood block detection of uncoded full response continuous phase modulation (CPM) over an additive white Gaussian noise (AWGN) channel. Both the maximum-likelihood metrics and the bit error probability performances of the associated detection algorithms are considered. The special and popular case of minimum-shift-keying (MSK) corresponding to h=0.5 and constant amplitude frequency pulse is treated separately. The many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance. >
TL;DR: In this paper, a precoding scheme for noise whitening on intersymbol interference (ISI) channels is presented, which is compatible with trellis-coded modulation and, unlike Tomlinson precoding, allows constellation shaping.
Abstract: A precoding scheme for noise whitening on intersymbol interference (ISI) channels is presented. This scheme is compatible with trellis-coded modulation and, unlike Tomlinson precoding, allows constellation shaping. It can be used with almost any shaping scheme, including the optimal SVQ shaping, as opposed to trellis precoding, which can only be used with trellis shaping. The implementation complexity of this scheme is minimal-only three times that of the noise prediction filter, hence effective noise whitening can be achieved by using a high-order predictor. >
TL;DR: In this paper, the effects of source finiteness, crustal wave propagation, and site response upon recorded strong ground motions from the 1989 Loma Prieta earthquake were assessed using band limited white noise (BLWN) with random vibration theory.
Abstract: The objective of this study is to assess the effects of source finiteness, crustal wave propagation, and site response upon recorded strong ground motions from the 1989 Loma Prieta earthquake. Our analysis uses band limited white noise (BLWN) with random vibration theory (RVT) to produce site‐specific estimates of peak acceleration and response spectral ordinates for both a point‐source and finite‐source model. Effects of nonlinear soil response are modeled through an equivalent‐linear approach. The point‐source model additionally accommodates crustal propagation effects in terms of direct‐plus‐postcritical reflections.
TL;DR: In this article, the authors consider linear regression of a random variable against general nonstochastic functions of time, but with error variables that form a serially correlated time series and examine the large sample properties defined by the partial sums of the regression residuals.
Abstract: It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression {2i- f(O)/fJr, f(A) dA), where f( ) is the spectral density of the noise process; in sample survey work this is known as the design effect or "deff." Simple precise adjustments to change-point test statistics which account for serial correlation are provided. The same adjustment applies to all commonly used regression models. Residual processes are derived for both stationary time series satisfying a moment condition and for general linear regression models with stationary error structure. 1. Introduction. Stochastic models for time sequenced data are generally characterized by several unknown parameters. These parameters may change over time, and if the changes, when they occur, do so unannounced and at unknown time points, then the associated inferential problem is referred to as the change-point problem. Various important application areas of statistics involve change detection in a central way; two of these areas are quality assurance and environmental monitoring. Most of the statistics commonly applied to the change-point problem involve cumulative sums or partial sums of regression residuals. The distribution theory for these statistics has been computed under the assumption that the error process for the regression model is white noise. In this paper we consider linear regression of a random variable against general nonstochastic functions of time, but with error variables that form a serially correlated time series. We then examine the large sample properties of the stochastic processes defined by the partial sums of the regression residuals. Large sample distribution theory for fixed sample size statistics used to detect changes in regression parameters is usually derived by computing the distributions of various functionals on
11 Oct 1993
TL;DR: The authors propose a multicarrier direct sequence spread spectrum system that is robustness against multipath fading, but to also achieve narrowband interference suppression; these advantages are obtained without the use of either an explicit RAKE structure or an interference suppression filter.
Abstract: The authors propose a multicarrier direct sequence spread spectrum system. By using this system, it is possible to get not only robustness against multipath fading, but to also achieve narrowband interference suppression; these advantages are obtained without the use of either an explicit RAKE structure or an interference suppression filter. The authors evaluate the performance of this system over both a frequency selective Rayleigh fading channel, and an additive white Gaussian noise channel in the presence of single tone interference. >
TL;DR: The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d.
Abstract: A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N/sup 2//2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise. >
TL;DR: In this article, the authors prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.
Abstract: We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.
TL;DR: A new mechanism generating long range temporal correlations in dynamical systems coupled to a source of white noise is discussed, and both Poisson statistics for events in log(time) and the 1/f power spectrum are found.
Abstract: We discuss a new mechanism generating long range temporal correlations in dynamical systems coupled to a source of white noise. The external noise induces dynamical events uncorrelated on a logarithmic time scale and produces a fluctuating output with ``1/f'' power spectrum. This behavior requires a complex phase space with many traps, which can arise due to strong cooperative effects. As a demonstration, we numerically analyze a system of many coupled degrees of freedom, which is externally driven and subject to a white noise perturbation. We find both Poisson statistics for events in log(time) and the 1/f power spectrum.
Patent•
27 May 1993
TL;DR: In this paper, a method and system for processing a set of data from an industrial process and/or a sensor is presented, which can include processing data from either real or calculated data related to an Industrial process variable.
Abstract: A method and system for processing a set of data from an industrial process and/or a sensor. The method and system can include processing data from either real or calculated data related to an industrial process variable. One of the data sets can be an artificial signal data set generated by an autoregressive moving average technique. After obtaining two data sets associated with one physical variable, a difference function data set is obtained by determining the arithmetic difference between the two pairs of data sets over time. A frequency domain transformation is made of the difference function data set to obtain Fourier modes describing a composite function data set. A residual function data set is obtained by subtracting the composite function data set from the difference function data set and the residual function data set (free of nonwhite noise) is analyzed by a statistical probability ratio test to provide a validated data base.
TL;DR: A computationally very efficient procedure for the estimation of time varying VAR model with time varying coefficients is developed by using the VAR representation with instantaneous response and the Kalman filter.