Time-varying Variance Research Articles

On some time-non-homogeneous diffusion approximations to queueing systems

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

The Cyclostationary Nature of Crosstalk Interference from Digital Signals in Multipair Cable--Part I: Fundamentals

This paper considers the cyclostationary nature of digital signals when determining crosstalk interference between such signals in multipair cable. This approach is necessary as the interference is only relevant at the decision instants in the receivers of the disturbed systems and any time variation of this interference with respect to the sampling instants changes the effect of this interference; previous studies in the area have ignored the cyclostationary nature of the digital signal. Expressions for the time-varying mean and variance of far-end and near-end crosstalk (FEXT and NEXT) have been derived. These expressions demonstrate the inherently smaller time variation of the NEXT interference when compared to the FEXT interference. An interesting result is that the calculation of the time-averaged value of the variance of FEXT and NEXT interference still requires the use of the cyclostationary properties of the digital signal. The results of this paper are extended and applied to various examples of the engineering of digital line systems in multipair cable in Part II of this paper.

Computation of changing variances

A method suitable for the processing of repetitive vibration signatures of unstable character has been found valuable in various applications. As it is based on a combination of time domain averaging of the signal and its variance, computational methods suitable for on-line or time-varying variances are of interest. Various schemes for such computations are suggested, differing mainly in the kind of averaging filter used. It is found that an estimated 25–70 samples are necessary for any such estimation of variances. Of the various schemes suggested, the one using filters with decaying memories has some desirable properties.