Asymptotic analysis of Cohen's equation for retrial queues in the Halfin-Whitt regime

No readable abstrac

Asymptotic analysis of Cohen's equation for retrial queues in the Halfin-Whitt regime

No readable abstrac

Convolution theory in a space of generalized functions

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The Zak transform and sampling theorems for wavelet subspaces

The Zak transform is used for generalizing a sampling theorem of G. Walter for wavelet subspaces. Cardinal series based on signal samples f(a+n), n ¿ Z with a possibly unequal to 0 (Walter's case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability of the resulting interpolation formula depends critically on a

Some theorems about the solutions of Stieltjes differential equations and the existence of optimal Stieltjes controllers

No abstract

A decay result for certain windows generating orthogonal Gabor bases

We consider tight Gabor frames (h,a=1,b=1) at critical density with h of the form Z -1(Zg/|Zg|). Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at 1/2,1/2, in [0,1)2. We show that h and its Fourier transform have maximal decay as allowed by the Balian-Low theorem. Our result illustrates a theorem of Benedetto, Czaja, Gadzinski, and Powell, case p=q=2, on sharpness of the Balian-Low theorem

Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes

This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples. The estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters. A statistical analysis shows that, for a burst of lost samples, the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity. The method is in fact the first step of an iterative algorithm, in which in each iteration step the current estimates of the missing samples are used to compute the new estimates. Furthermore, the feasibility of implementation in hardware for real-time use is established. The method has been tested on artificially generated auto-regressive processes as well as on digitized music and speech signals

On positivity of time-frequency distributions.

Consideration is given to the problem of how to regard the fundamental impossibility with time-frequency energy distributions of Cohen's class always to be nonnegative and, at the same time, to have correct marginal distributions. It is shown that the Wigner distribution is the only member of a large class of bilinear time-frequency distributions that becomes nonnegative after smoothing in the time-frequency plane by means of Gaussian weight functions with BT product equal to unity