White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

A simple white noise analysis of neuronal light responses.

Abstract: A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

Statistical analysis of stationary time series

Abstract: Stationary Stochastic Processes and Their Representations: 1.0 Introduction 1.1 What is a stochastic process? 1.2 Continuity in the mean 1.3 Stochastic set functions of orthogonal increments 1.4 Orthogonal representations of stochastic processes 1.5 Stationary processes 1.6 Representations of stationary processes 1.7 Time and ensemble averages 1.8 Vector processes 1.9 Operations on stationary processes 1.10 Harmonizable stochastic processes Statistical Questions when the Spectrum is Known (Least Squares Theory): 2.0 Introduction 2.1 Preliminaries 2.2 Prediction 2.3 Interpolation 2.4 Filtering of stationary processes 2.5 Treatment of linear hypotheses with specified spectrum Statistical Analysis of Parametric Models: 3.0 Introduction 3.1 Periodogram analysis 3.2 The variate difference method 3.3 Effect of smoothing of time series (Slutzky's theorem) 3.4 Serial correlation coefficients for normal white noise 3.5 Approximate distributions of quadratic forms 3.6 Testing autoregressive schemes and moving averages 3.7 Estimation and the asymptotic distribution of the coefficients of an autoregressive scheme 3.8 Discussion of the methods described in this chapter Estimation of the Spectrum: 4.0 Introduction 4.1 A general class of estimates 4.2 An optimum property of spectrograph estimates 4.3 A remark on the bias of spectrograph estimates 4.4 The asymptotic variance of spectrograph estimates 4.5 Another class of estimates 4.6 Special estimates of the spectral density 4.7 The mean square error of estimates 4.8 An example from statistical optics Applications: 5.0 Introduction 5.1 Derivations of spectra of random noise 5.2 Measuring noise spectra 5.3 Turbulence 5.4 Measuring turbulence spectra 5.5 Basic ideas in a statistical theory of ocean waves 5.6 Other applications Distribution of Spectral Estimates: 6.0 Introduction 6.1 Preliminary remarks 6.2 A heuristic derivation of a limit theorem 6.3 Preliminary considerations 6.4 Treatment of pure white noise 6.5 The general theorem 6.6 The normal case 6.7 Remarks on the nonnormal case 6.8 Spectral analysis with a regression present 6.9 Alternative estimates of the spectral distribution function 6.10 Alternative statistics and the corresponding limit theorems 6.11 Confidence band for the spectral density 6.12 Spectral analysis of some artificially generated time series Problems in Linear Estimation: 7.0 Preliminary discussion 7.1 Estimating regression coefficients 7.2 The regression spectrum 7.3 Asymptotic expression for the covariance matrices 7.4 Elements of the spectrum 7.5 Polynomial and trigonometric regression 7.6 More general trigonometric and polynomial regression 7.7 Some other types of regression 7.8 Detection of signals in noise 7.9 Confidence intervals and tests Assorted Problems: 8.0 Introduction 8.1 Prediction when the conjectured spectrum is not the true one 8.2 Uniform convergence of the estimated spectral density to the true spectral density 8.3 The asymptotic distribution of an integral of a spectrograph estimate 8.4 The mean square error of prediction when the spectrum is estimated 8.5 Other types of estimates of the spectrum 8.6 The zeros and maxima of stationary stochastic processes 8.7 Prefiltering of a time series 8.8 Comments on tests of normality Problems Appendix on complex variable theory Bibliography Index.

Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging

Abstract: Noise spectrum estimation is a fundamental component of speech enhancement and speech recognition systems. We present an improved minima controlled recursive averaging (IMCRA) approach, for noise estimation in adverse environments involving nonstationary noise, weak speech components, and low input signal-to-noise ratio (SNR). The noise estimate is obtained by averaging past spectral power values, using a time-varying frequency-dependent smoothing parameter that is adjusted by the signal presence probability. The speech presence probability is controlled by the minima values of a smoothed periodogram. The proposed procedure comprises two iterations of smoothing and minimum tracking. The first iteration provides a rough voice activity detection in each frequency band. Then, smoothing in the second iteration excludes relatively strong speech components, which makes the minimum tracking during speech activity robust. We show that in nonstationary noise environments and under low SNR conditions, the IMCRA approach is very effective. In particular, compared to a competitive method, it obtains a lower estimation error, and when integrated into a speech enhancement system achieves improved speech quality and lower residual noise.

Attractors for random dynamical systems

Abstract: A criterion for existence of global random attractors for RDS is established. Existence of invariant Markov measures supported by the random attractor is proved. For SPDE this yields invariant measures for the associated Markov semigroup. The results are applied to reation diffusion equations with additive white noise and to Navier-Stokes equations with multiplicative and with additive white noise.

Probability of error in MMSE multiuser detection

Abstract: The performance analysis of the minimum-mean-square-error (MMSE) linear multiuser detector is considered in an environment of nonorthogonal signaling and additive white Gaussian noise. In particular, the behavior of the multiple-access interference (MAI) at the output of the MMSE detector is examined under various asymptotic conditions, including: large signal-to-noise ratio; large near-far ratios; and large numbers of users. These results suggest that the MAI-plus-noise contending with the demodulation of a desired user is approximately Gaussian in many cases of interest. For the particular case of two users, it is shown that the maximum divergence between the output MAI-plus-noise and a Gaussian distribution having the same mean and variance is quite small in most cases of interest. It is further proved in this two-user case that the probability of error of the MMSE detector is better than that of the decorrelating linear detector for all values of normalized crosscorrelations not greater than 1/2 /spl radic/(2+/spl radic/3)/spl cong/0.9659.