White noise

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

The estimation of the frequency response function of a mechanoreceptor

Abstract: Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.

A geometric approach to multiple-channel signal detection

Abstract: The paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of the GC estimate is exploited to derive its distribution under the H/sub 0/ hypothesis that the data channels contain independent white Gaussian noise sequences. Detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution. The relationship of the H/sub 0/ distribution of the GC estimate to that of the determinant of a complex Wishart-distributed matrix is noted. The detection performance of the three-channel GC estimate is evaluated by simulation using a white Gaussian signal sequence in white Gaussian noise. Its performance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic. The GC approach is found to provide better detection performance than the MC approach in terms of the minimum signal-to-noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities. >

Estimation of the number of sources in unbalanced arrays via information theoretic criteria

Abstract: Estimating the number of sources impinging on an array of sensors is a well-known and well-investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and nonrobust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years, several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multidimensional searches. In this paper, which is motivated by real-life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL-type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multidimensional searches is presented as well, making this estimator a favorable choice for practical applications.

An improved complementary ensemble empirical mode decomposition with adaptive noise and its application to rolling element bearing fault diagnosis.

Abstract: A novel time–frequency analysis method called complementary complete ensemble empirical mode decomposition (EEMD) with adaptive noise (CCEEMDAN) is proposed to analyze nonstationary vibration signals. CCEEMDAN combines the advantages of improved EEMD with adaptive noise and complementary EEMD, and it improves decomposition performance by reducing reconstruction error and mitigating the effect of mode mixing. However, because white noise mixed in with the raw vibration signal covers the whole frequency bandwidth, each mode inevitably contains some mode noise, which can easily inundate the fault-related information. This paper proposes a time–frequency analysis method based on CCEEMDAN and minimum entropy deconvolution (MED) for fault detection of rolling element bearings. First, a raw signal is decomposed into a series of intrinsic mode functions (IMFs) by using the CCEEMDAN method. Then a sensitive parameter (SP) based on adjusted kurtosis and Pearson’s correlation coefficient is applied to select a sensitive mode that contains the most fault-related information. Finally, the MED is applied to enhance the fault-related impulses in the selected IMF. The fault signals of high-speed train axle-box bearing are applied to verify the effectiveness of the proposed method. Results show that the proposed method can effectively reveal axle-bearing defects’ fault information. The comparisons illustrate the superiority of SP over kurtosis for selecting the sensitive mode from the resulted signal of CCEEMEDAN. Further, we conducted comparisons that highlight the superiority of our proposed method over individual CCEEMDAN and MED methods and over two other popular signal-processing methods, variational mode decomposition and fast kurtogram.

Multifractional processes with random exponent

Abstract: Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Holder regularity and their self-similarity.