Topic
White noise
About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.
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TL;DR: In this paper, an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series is presented, where the best k tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived.
Abstract: We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best K tapers creates K time series. A decaying sinusoid model is fit to the K time series by a least squares procedure. A statistical F-test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillations in the data. The F-test is performed at a number of chosen frequencies, producing a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a cosine-tapered time-series. The multiple-taper method is found to be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.
111 citations
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TL;DR: The test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis and is shown to be able to resolve closely spaced sinusoids at lower signal-to-noise ratios than heuristic tests.
Abstract: The test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis. The estimator is shown to be able to resolve closely spaced sinusoids at lower signal-to-noise ratios than heuristic tests. Simulation results for two closely spaced sinusoids are detailed. Several unanswered questions are discussed. >
111 citations
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29 Apr 2002
TL;DR: Signals Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise Signal Characteristics of Signals at the Generalization Detector Output under under the Stochastic Distribution Law of the Signal Probability Distribution Density.
Abstract: PROBABILITY AND STATISTICS Probability: Basic Concepts Random Variables Stochastic Processes Correlation Function Spectral Density Statistical Characteristics Conclusions References CLASSICAL AND MODERN APPROACHES TO SIGNAL DETECTION THEORY Gaussian Approach Markov Approach Bayes' Decision-Making Rule Unbiased and Invariant Decision-Making Rules Mini-Max Decision-Making Rule Sequential Signal Detection Signal Detection in Non-Gaussian Noise Non-Parametric Signal Detection Conclusions References MAIN CHARACTERISTICS OF MULTIPLICATIVE NOISE Classification of the Noise and Interference Sources of the Multiplicative Noise Classification and Main Properties of Multiplicative Noise Correlation Function and Energy Spectrum of Multiplicative Noise Generalized Statistical Model of Multiplicative Noise Conclusions References STATISTICAL CHARACTERISTICS OF SIGNALS UNDER THE STIMULUS OF MULTIPLICATIVE NOISE Deterministic and Quasideterministic Multiplicative Noise Stationary Fluctuating Multiplicative Noise Ensemble and Individual Realizations of the Signal Probability Distribution Density of the Signal in the Additive Gaussian Noise under the Stimulus of Multiplicative Noise Multivariate Probability Distribution Density of Instantaneous Values of the Signal under the Stimulus of Fluctuating Multiplicative Noise Conclusions References MAIN THEORETICAL PRINCIPLES OF THE GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE Basic Concepts Criticism Initial Premises Likelihood Ratio Engineering Interpretation Generalized Detector Distribution Law Conclusions References GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE AND LINEAR SYSTEMS Signal Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise Signal Characteristics at the Generalized Detector Output under under the Stimulus of Multiplicative Noise Signal Noise Component for Some Types of Signals Signal Noise Component under the Stimulus of the Slow and Rapid Multiplicative Noise Signal Distribution Law under the Stimulus of Multiplicative Noise Conclusions References GENERALIZED APPROACH TO SIGNAL DETECTION IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE GAUSSIAN NOISE Statistical Characteristics of Signals at the Output of the Generalized Detector Detection Performances of the Generalized Detector Known Correlation Function of the Multiplicative Noise One-Channel Generalized Detector Diversity Signal Detection Conclusions References SIGNAL PARAMETER MEASUREMENT PRECISION A Single Signal Parameter Measurement under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise Simultaneous Measurement of Two Signal Parameters under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise A Single Parameter Measurement under a Combined Stimulus of High Multiplicative and Additive Gaussian Noise Conclusions References SIGNAL RESOLUTION UNDER THE GENERALIZED APPROACH TO SIGNAL PROCESSING IN THE PRESENCE OF NOISE Estimation Criteria of Signal Resolution Signal Resolution by Woodward Criterion Statistical Criterion of Signal Resolution Conclusions References APPENDIX I: Delta Function APPENDIX II: Correlation Function and Energy Spectrum of Noise Modulation Function NOTATION INDEX INDEX
111 citations
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TL;DR: In this article, a sufficiently rich class of nonlinear functionals of white noise, e.g., the Wiener process, were obtained by studying riggings of the L 2 space with the white noise measure.
110 citations
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27 Jun 1994
TL;DR: In this article, the second and fourth order moments of the observed noisy signal are used to estimate the SNR of the noisy signal, and shape factors of the signal's and the noise's probability density functions are used.
Abstract: An algorithm is presented that allows an estimation of the SNR just by the observation of the noisy signal. For the estimation, shape factors of the signal's and the noise's probability density functions are used. The algorithm is based on the second and fourth order moments of the observed noisy signal. >
110 citations