White noise

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

Consistent Estimates of the Parameters of a Linear System

Abstract: : The paper considers the identification of the transition matrix and statistical parameters of a discrete linear system excited by white noise. Estimates of these parameters are derived and shown to be strongly consistent. It is further shown that when strongly consistent estimates are used in the Kalman Filter equations that the Kalman Filter parameters and the state variable estimates so obtained are also strongly consistent. (Author)

Linear Serial Rank Tests for Randomness Against Arma Alternatives

Abstract: In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided. Finally, we study the asymptotic relative efficiency of the proposed procedures with respect to their normal theory counterparts based on sample autocorrelations.

Development and application of white-noise modeling techniques for studies of insect visual nervous system.

Abstract: The nonlinear system identification technique through white-noise stimulation is extended to multi-input, -output systems with consideration given to applications in the functional study of the nervous system. The applicability of the method is discussed in general and in particular for the motion detection neuronal system of the fly. Two series of experiments are performed; one with moving striped-pattern stimuli and the other with spot stimuli of fluctuating intensity. In both cases nonlinear dynamic models are derived which describe the system with considerable accuracy over the frequency range of 0.2–50 Hz and a dynamic amplitude range of about 40-1. These models are able to predict accurately all the discrete experiments so far performed on this system for which the models are applicable. The differences in dynamic characteristics between the corresponding system of the Musca and Phoenicia families of flies are minor except for a difference in latencies and if the difference in geometry of their faceted eyes is taken into account. The large field response of the motion detection unit is a linear weighted summation of all the smaller field highly nonlinear subsystems of which the large field is comprised.

A solution to the problem of spontaneous line splitting in maximum entropy power spectrum analysis

Abstract: Under certain conditions, Burg maximum entropy spectra of sampled sine waves, in the presence of additive Gaussian white noise, show either spontaneous line splitting (at low noise levels) or appreciable frequency shifting (at moderate noise levels). This difficulty arises because an unnecessary constraint is imposed during the minimization of the prediction error power. When the constraint is relaxed and a lighter one imposed, the error power decreases and the problem is solved. The nature of the constraint is discussed, and the mathematical details of the new method are presented. The new method is verified by using a few simple test cases in which spontaneous line splitting is healed or frequency shifting is reduced drastically (Fougere, 1975).

Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs

Abstract: We present electroelastic modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The modeling approach employed herein is based on a distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included, since broadband random vibrations, such as Gaussian white noise, might excite higher vibration modes. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given power spectral density (PSD) or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first of the two numerical solution methods employs the Fourier series representation of the base acceleration history in an ordinary differential equation solver while the second method uses an Euler‐Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The simulations exhibit very good agreement with the experimental measurements for a range of resistive electrical boundary conditions and input PSD levels. It is also shown that lightly damped higher vibration modes can alter the expected power curve under broadband random excitation. Therefore, the distributed-parameter modeling and solutions presented herein can be used as a more accurate alternative to the existing single-degree-of-freedom solutions for broadband random vibration energy harvesting.