This tutorial treats mixtures of Gaussian probability distribution functions. Gaussian mixtures are combinations of a finite number of Gaussian distributions. They are used to model complex multidimensional distributions. When there is a need to learn the parameters of the Gaussian mixture, the EM algorithm is used. In the second part of this tutorial mixtures of Gaussian are used to model the ...

Gaussian elements. The hypothesis that random non-stationary vehicle vibrations are essentially composed of a sequence of zero-mean random Gaussian processes of varying standard deviations is tested and the paper reveals that the variations in the magnitude of the vibrations are the cause of the leptokurtic, non-Gaussian nature of the process. It is shown how non-stationary vibration signals ca...

| A procedure for estimating the joint probability density function (pdf) of T 1 , T 2 , and proton spin density (P D) for gray matter (GM), white matter (WM), and cerebrospinal uid (CSF) in the brain is presented. The pdf's have numerous applications, including the study of tissue parameter variability in pathology and across populations. The procedure requires a multispectral, spin echo magne...

This tutorial treats mixtures of Gaussian probability distribution functions. Gaussian mixtures are combinations of a finite number of Gaussian distributions. They are used to model complex multi-dimensional distributions. When there is a need to learn the parameters of the Gaussian mixture, the EM algorithm is used. In the second part of this tutorial mixtures of Gaussian are used to model the...

My original query some time ago – one computer crash ago was about the amplitude probability density function (pdf) of surface EMG data (from which we have subtracted the mean value). That is, if one plots the amplitude of the rectified EMG in an histogram, what does it look like? The common assumption is that we get a (one-sided) Gaussian pdf for stationary data. This is generally so. However,...

The equalisation topic is well researched and a variety of solutions are available. The MAP sequence detector provides the lowest symbol error rate (SER) attainable, and the MLSE offers a near optimal solution. However, these optimal techniques are not yet practical for high-level modulation schemes, due to their computational complexity. Linear equaliser or linear-combiner DFE are practical sc...

Introduction: The non-Gaussian noise in the practical world can be well characterised by its impulsive nature. Typical impulsive interference may include atmospheric noise, ambient acoustic noise and lightning, switching transients, etc. Since 1993, there has been tremendous interest in the class of symmetric a-stable (SaS) distributions [1], as a generalisation of Gaussian distribution, which ...

We consider narrowband angle of arrival estimation in nonGaussian (NG) noise channels, such as arises in some indoor and outdoor mobile communications channels. We develop a general expression for the Cramer-Rao bound (CRB) for direction nding using arrays for deterministic signals plus iid non-Gaussian noise, generalizing the Gaussian CRB. The CRBs for the noise and direction parameters decoup...

In most existing transmitted-reference ultra-wideband (TR-UWB) communication systems, receivers use the standard Gaussian approximation (SGA) for multiuser interference (MUI). It is an assumption used in most conventional multiuser systems, where the MUI tends to a Gaussian process by the central limit theorem, and convergence is relatively fast with respect to the number of users. However, for...

A difference approximation that is second-order accurate in the time step h is derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then...