An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Two-stage queuing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application