Showing papers on "White noise published in 1996"

Statistical theory of quantization

Abstract: The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floating-point quantization is demonstrated.

A vector Taylor series approach for environment-independent speech recognition

Abstract: In this paper we introduce a new analytical approach to environment compensation for speech recognition. Previous attempts at solving analytically the problem of noisy speech recognition have either used an overly-simplified mathematical description of the effects of noise on the statistics of speech or they have relied on the availability of large environment-specific adaptation sets. Some of the previous methods required the use of adaptation data that consists of simultaneously-recorded or "stereo" recordings of clean and degraded speech. In this work we introduce the use of a vector Taylor series (VTS) expansion to characterize efficiently and accurately the effects on speech statistics of unknown additive noise and unknown linear filtering in a transmission channel. The VTS approach is computationally efficient. It can be applied either to the incoming speech feature vectors, or to the statistics representing these vectors. In the first case the speech is compensated and then recognized; in the second case HMM statistics are modified using the VTS formulation. Both approaches use only the actual speech segment being recognized to compute the parameters required for environmental compensation. We evaluate the performance of two implementations of VTS algorithms using the CMU SPHINX-II system on the 100-word alphanumeric CENSUS database and on the 1993 5000-word ARPA Wall Street Journal database. Artificial white Gaussian noise is added to both databases. The VTS approaches provide significant improvements in recognition accuracy compared to previous algorithms.

Asymptotic equivalence of nonparametric regression and white noise

Abstract: The principal result is that, under conditions, to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems, and conversely. This asymptotic equivalence is in a global and uniform sense. Any normalized risk function attainable in one problem is asymptotically attainable in the other, with the difference in normalized risks converging to zero uniformly over the entire parameter space. The results are constructive. A recipe is provided for producing these asymptotically equivalent procedures. Some implications and generalizations of the principal result are also discussed.

Ecology, evolution and 1 f -noise

Abstract: Among ecologists, there has been a growing recognition of the importance of long-term correlations In environmental time series The family of 1 f -noises - fluctuations defined in terms of the different timescales present - is a useful approach to this problem White noise and the random walk, the two currently favoured descriptions of environmental fluctuations, lie at extreme ends of this family of processes Recent analyses of data, results of models, and examination of basic 1 f -noise properties, suggest that pink 1 f noise, which lies midway between white noise and the random walk, might be the best null model of environment variation If true, this would have important consequences for the interpretation of ecological time series and for ecological and evolutionary modelling

Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise

Abstract: The random attractor to the stochastic 3D Navier-Stokes equation will be studied. In the first part we formulate an existence theorem for attractors of non-autonomous dynamical systems on a bundle of metric spaces. Using this theorem we can prove the existence of an attractor for the 3D Navier-Stokes equation with multiplicative white noise. In addition we prove that this attractor is a random multi-function

Advanced Signal Processing and Digital Noise Reduction

Abstract: Introduction to Signal Processing and Noise Reduction Stochastic Processes and Statistical Characterization of Signals Signal Transforms Bayesian Probabilistic Estimation Theory Wiener Filters and Kalman Filters Linear Prediction Models Sample-Adaptive Least Squared Error Filters Power Spectrum Estimation Finite-State Statistical Models for Non-stationary Stochastic Processes Interpolation of a Sequence of Samples Modelling, Detection and Removal of Impulsive Noise Spectral Subtraction Removal of Transient Noise Pulses Echo Cancellation and Multi-Input Adaptive Noise Reduction Adaptive Notch Filters Channel Equalization Noise Compensation for Speech Recognition in Adverse Environments.

Asymptotic Equivalence of Density Estimation and Gaussian White Noise

Abstract: Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam's deficiency distance $\Delta$ would make it precise. The models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. In nonparametrics, a first result of this kind has recently been established for Gaussian regression. We consider the analogous problem for the experiment given by n i.i.d. observations having density f on the unit interval. Our basic result concerns the parameter space of densities which are in a Holder ball with exponent $\alpha > 1/2$ and which are uniformly bounded away from zero. We show that an i. i. d. sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift $f^{1/2}$ and variance $1/4 n^{-1}$. This represents a nonparametric analog of Le Cam's heteroscedastic Gaussian approximation in the finite dimensional case. The proof utilizes empirical process techniques related to the Hungarian construction. White noise models on f and log f are also considered, allowing for various "automatic" asymptotic risk bounds in the i.i.d. model from white noise.

Nearest neighbor decoding for additive non-Gaussian noise channels

Abstract: We study the performance of a transmission scheme employing random Gaussian codebooks and nearest neighbor decoding over a power limited additive non-Gaussian noise channel. We show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white Gaussian noise channel with signal and noise power equal to those of the original channel. The results are presented for single-user channels as well as multiple-access channels, and are extended to fading channels with side information at the receiver.

Noise Colour and the Risk of Population Extinctions

Abstract: A recurrent problem in ecology and conservation biology is to estimate the risk of population extinctions. Extinction probabilities are not only imperative for conservation and management, but may also elucidate basic mechanisms of the regulation of natural populations (Burgman et al. 1993; Pimm 1994). The usual way of modelling stochastic influence on population dynamics has been to assume that the external noise is uncorrelated. This means that each and every randomly drawn noise value is totally independent on previous ones. This is what is generally called \`white' noise. However, the noise itself can be temporally autocorrelated. That is, the values of the random numbers used in the noise process will depend on previous ones. Here we show that the autocorrelation, or colour, of the external noise assumed to influence population dynamics strongly modifies estimated extinction probabilities. For positively autocorrelated (\`red') noise, the risk of extinction clearly decreases the stronger the autocorrelation is. Negatively autocorrelated (`blue') noise is more ambiguously related to extinction probability. Thus, the commonly assumed white noise in population modelling will severely bias population extinction risk estimates. Moreover, the extinction probability estimates are also significantly dependent on model structure which calls for a cautious use of traditional discrete-time models.

Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise: application to parameter estimation and empirical robustness analysis

Abstract: The strong tracking filter (STF) proposed by Zhou et al. in 1992, which was developed for nonlinear systems with white noise, is extended to a class of nonlinear time-varying stochastic systems with coloured noise. A new concept of‘softening factor’is introduced to make the state estimator much smoother; its value can be preselected by computer simulations via a heuristic searching scheme. The STF is then used to estimate the parameters of a class of nonlinear time-varying stochastic systems in the presence of coloured noise. The robustness against model uncertainty of the STF is thoroughly studied via Monte Carlo simulations. The results show that the STF has strong robustness against model-plant parameter mismatches in the statistics of the initial conditions, the statistics of the process noise and the measurement noise, the system parameters, and the parameters in the measurement noise model. To a great extent the STF can give bias-free parameter estimations, where the parameters may be randomly time ...

A deterministic digital simulation model for Suzuki processes with application to a shadowed Rayleigh land mobile radio channel

Abstract: We present a novel computer simulation model for a land mobile radio channel. The underlying channel model takes for granted non-frequency-selective fading but considers the effects caused by shadowing. For such a channel model we design a simulation model that is based on an efficient approximation of filtered white Gaussian noise processes by finite sums of properly weighted sinusoids with uniformly distributed phases. In all, four completely different methods for the computation of the coefficients of the simulation model are introduced. Furthermore, the performance of each procedure is investigated on the basis of two quality criteria. All the presented methods have in common the fact that the resulting simulation model has a completely determined fading behavior for all time. Therefore, the simulation model can be interpreted as a deterministic model that approximates stochastic processes such as Rayleigh, log-normal, and Suzuki (1977) processes.

Wavelet Analysis and Synthesis of Stationary Long-Memory Processes

Abstract: The discrete wavelet transform (DWT) can be interpreted as a filtering of a time series by a set of octave band filters such that the width of each band as a proportion of its center frequency is constant. A long-memory process having a power spectrum that plots as a straight line on log-frequency/log-power scales over many octaves of frequency is intrinsically related to such a structure. As an example of such processes, we focus on one class of discrete-time, stationary, long-memory processes, the fractionally differenced Gaussian white noise processes (fdGn). We show how the DWT breaks down a fdGn, and show the exact correlation structure of the resulting coefficients for different wavelets (Daubechies' minimum-phase and least-asymmetric and Haar). The DWT is an impressive “whitening filter.” A discrete wavelet-based scheme for simulating fdGn's is discussed and is shown to be equivalent to a spectral decomposition of the covariance matrix of the process; however, it can be carried out using o...

A model selection rule for sinusoids in white Gaussian noise

Abstract: The model selection problem for sinusoidal signals has often been addressed by employing the Akaike (1974) information criterion (AIC) and the minimum description length principle (MDL). The popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented. They can, however, produce misleading results if they are not carefully used. The AIC and MDL have a common form in that they comprise two terms, a data term and a penalty term. The data term quantifies the residuals of the model, and the penalty term reflects the desideratum of parsimony. While the data terms of the AIC and MDL are identical, the penalty terms are different. In most of the literature, the AIC and MDL penalties are, however, both obtained by apportioning an equal weight to each additional unknown parameter, be it phase, amplitude, or frequency. By contrast, we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies. Following the Bayesian methodology, we derive a model selection criterion for sinusoidal signals in Gaussian noise which also contains the log-likelihood and the penalty terms. The simulation results disclose remarkable improvement in our selection rule over the commonly used MDL and AIC.

Asymptotic Stability of the Optimal Filter with Respect toIts Initial Condition

Abstract: Consider the problem of estimation of a diffusion signal observed in additive white noise. If the solution to the filtering equations, initialized with an incorrect prior distribution, approaches the true conditional distribution asymptotically in time, then the filter is said to be asymptotically stable with respect to perturbations of the initial condition. This paper presents asymptotic stability results for linear filtering problems and for signals with limiting ergodic behavior. For the linear case, stability of the Riccati equation of Kalman filtering is used to derive almost sure asymptotic stability of linear filters for possibly non-Gaussian initial conditions. In the nonlinear case, asymptotic stability in a weak convergence sense is shown for filters of signal diffusions which converge in law to an invariant distribution.

Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals

Abstract: The high-order ambiguity function (HAF) is a nonlinear operator designed to detect, estimate, and classify complex signals whose phase is a polynomial function of time. The HAF algorithm, introduced by Peleg and Porat (1991), estimates the phase parameters of polynomial-phase signals measured in noise. The purpose of this correspondence is to analyze the asymptotic accuracy of the HAF algorithm in the case of additive white Gaussian noise. It is shown that the asymptotic variances of the estimates are close to the Cramer-Rao bound (CRB) for high SNR. However, the ratio of the asymptotic variance and the CRB has a polynomial growth in the noise variance.

Analysis of nonlinear FM signals by pattern recognition of their time-frequency representation

Abstract: The aim is to propose a method for detection and parameter estimation of nonlinear FM signals, mono- or multicomponent, embedded in white Gaussian noise. The proposed approach consists in mapping the signal into the time-frequency plane by a time-frequency distribution with reassignment, and then in applying a pattern recognition technique, like the Hough transform, to the time-frequency representation to recognize specific shapes. The advantages of this method over the conventional maximum likelihood estimator are (1) a simpler implementation, because it reduces the dimension of the search space and (2) a consistent attenuation of the interference terms between different components of a signal or between signal and noise.

Codebook constrained Wiener filtering for speech enhancement

Abstract: Speech enhancement using iterative Wiener filtering has been shown to require interframe and intraframe constraints in all-pole parameter estimation We show that a clean speech VQ codebook is more effective in providing intraframe constraints and, hence, better convergence of the iterative filtering scheme Satisfactory speech enhancement results are obtained with a small codebook of 128, and the algorithm is effective for both white noise and pink noise up to 0 dB SNR

Signal detection statistics of stochastic resonators.

Abstract: We consider the signal detection performance of networks of coupled overdamped nonlinear dynamic elements driven by a weak sinusoidal signal embedded in Gaussian white noise. In the "stochastic resonance" operating regime, (1) the detection performance exhibits a maximum reflecting the maximum in the signal-to-noise ratio, and (2) coupling significantly enhances the detection performance over that of a single element. Coupling-induced linearization allows the nonlinear system to approach the performance of the linear system which is optimal for our signal detection problem.

Spatiotemporal stochastic resonance in a phi 4 model of kink-antikink nucleation

Abstract: The synchronization and signal processing properties of a linearly coupled chain of N overdamped bistable elements, subject to a deterministic periodic signal and uncorrelated white noise, are addressed in the continuum limit of a f4 field theory. The scaling relations for the optimum noise and coupling strengths that correspond to the observed spatiotemporal stochastic resonance are derived via the f4 theory and shown to conform to the results of earlier numerical simulations in the large N limit.

Multiplicative stochastic resonance in linear systems: Analytical solution

Abstract: The maximum of a signal as a function of the noise intensity ("stochastic resonance") is found in a linear system subjected to multiplicative colour noise. This result is obtained for an arbitrary dichotomous noise and for a colour noise with a short autocorrelation time. Stochastic resonance does not occur for Gaussian white noise.

Tracking maneuvering targets with multiple sensors: does more data always mean better estimates?

Abstract: In many multisensor systems the number and type of sensors supporting a particular target track can vary with time due to the mobility, type, and resource limitations of the individual sensors. This variability in the configuration of the sensor system poses a significant problem when tracking maneuvering targets because of the uncertainty in the target motion model. A Kalman filter is often employed to filter the position measurements for estimating the position, velocity, and acceleration of a target. When designing the Kalman filter, the process noise (acceleration) variance Q/sub k/ is selected such that the 65 to 95% probability region contains the maximum acceleration level of the target. However, when targets maneuver, the acceleration changes in a deterministic manner. Thus, the white noise assumption associated with the process noise is violated and the filter develops a bias in the state estimates during maneuvers. The problem of tracking maneuvering targets with multiple sensors is illustrated through an example involving target motion in a single coordinate in which it is shown that with two sensors one can have (under certain conditions that include perfect alignment of the sensors) worse track performance than a single sensor. The Interacting Multiple Model (IMM) algorithm is applied to the illustrative example to demonstrate a potential solution to this problem of track filter performance.

Testing for Serial Correlation against an ARMA(1,1) Process

Abstract: This article is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against autoregressive moving average model ARMA(1, 1) alternatives is considered. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are shown to be asymptotically admissible for ARMA(1, 1) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white noise alternatives. Simulation results compare the tests to several tests in the literature. These results show that the LR and Exp-LR∞ tests have very good all-around power properties for nonseasonal alternatives.

Residual modeling in music analysis-synthesis

Abstract: In analysis-synthesis of musical sounds based on a sinusoidal model, the difference between the original signal and the synthesized signal, termed the residual, is typically a broadband noise process. It contains such musical phenomena as flute breath noise or violin bow noise. Synthesis without such "noise" tends to sound artificial; it is desirable to improve the synthesis realism by modeling the residual in such a way that it can be reinjected in the synthesized signal. This paper deals with a model of noise perception based on the equivalent rectangular bands (ERBs) of the auditory system. Since a broadband noise is perceptually well-represented by the time-varying energy in each of these frequency bands, the residual is parametrized in terms of these energies in the proposed model. An application of the model to music synthesis based on the inverse fast Fourier transform (FFT) is described in detail.

Linear unbiased state estimation for random models with sensor delay

Abstract: The motivation for the work reported in this paper accrues from the necessity of finding stabilizing control laws for systems with randomly varying distributed delays. It reports the development of full and reduced order linear unbiased estimators for discrete-time stochastic parameter systems and shows how to parametrize the estimator gains to achieve a certain estimation error covariance. Both finite-time and steady-state estimators are considered. The results are potentially applicable to state-estimate feedback control schemes for such systems.

An expert system for testing industrial processes and determining sensor status

Abstract: A method and system (110) for monitoring both an industrial process and a sensor (104). The method and system include determining a minimum number of sensor pairs needed to test the industrial process as well as the sensor (104) for evaluating the state of operation of both. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the pair of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.