White noise

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

Qualitative Theory of Stochastic Systems

Abstract: Publisher Summary This chapter presents the problems and results of the qualitative theory of stochastic dynamical systems. Qualitative theory studies the general nature of a solution in the entire time interval. Attention has been attracted mainly by the white noise case, in particular, by nondegenerate diffusion processes. The methods used were mainly Lyapunov function techniques and the interrelation between Markov processes and deterministic partial differential equations. White noise is a generalized Gaussian stationary process with constant spectral density on the whole real line. Qualitative theory studies the general nature of a solution on the entire time interval (asymptotic or long-term behavior) without solving the equation.

A Note on Trend Removal Methods: The Case of Polynomial Regression versus Variate Differencing

Abstract: This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion. On the other hand, we show that the regression residuals from the linear detrending of a random walk series would contain large positive autocorrelations in the first few lags. Relative to that of white noises, the SDF of the regression residuals would be exaggerated at the low frequency portion and attenuated at the high frequency portion.

Stochastic Averaging of Energy Envelope

Abstract: The method of stochastic averaging, as applied previously to analyze the energy envelope of a nonlinear system under random excitations of independent ideal Gaussian white noises, is generalized to...

A method for modifying the image quality parameters of digital radiographic images.

Abstract: A new computer simulation approach is presented that is capable of modeling several varieties of digital radiographic systems by their image quality characteristics. In this approach, the resolution and noise characteristics of ideal supersampled input images are modified according to input modulation transfer functions (MTFs) and noise power spectra (NPS). The modification process is separated into two routines-one for modification of the resolution and another for modification of the noise characteristics of the input image. The resolution modification routine blurs the input image by applying a frequency filter described by the input MTF. The resulting blurred image is then reduced to its final size to account for the sampling process of the digital system. The noise modification routine creates colored noise by filtering the frequency components of a white noise spectrum according to the input noise power. This noise is then applied to the image by a moving region of interest to account for variations in noise due to differences in attenuation. In order to evaluate the efficacy of the modification routines, additional routines were developed to assess the resolution and noise of digital images. The MTFs measured from the output images of the resolution modification routine were within 3% of the input MTF The NPS measured from the output images of the noise modification routine were within 2% of the input NPS. The findings indicate that the developed modification routines provide a good means of simulating the resolution and noise characteristics of digital radiographic systems for optimization or processing purposes.