In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequalit...

The majority of literature on robust control assumes that a design model is available and that the uncertainty model bounds the actual variations about the nominal model. However, methods for generating accurate design models have not received as much attention in the literature. The influence of the level of accuracy of the uncertainty model on closed loop performance has received even less at...

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg’s uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining an “uncertainty” lower bound. Taking the variance as a measure of localization in time and frequency, Gaussian functions reach this bound for ...

The frequency and duration of microbial contamination events in the environment in which ready-to-eat (RTE) foods are exposed for processing and packaging is subject to uncertainty and variability. Variability, within-model parameter uncertainty, and uncertainty regarding model selection are formally considered in modeling the frequency and duration of such contamination events by Listeria spec...

Global warming and then climate change are important topics studied by researchers throughout the world in the recent decades. In these studies, climatic parameters changes are investigated. Considering large-scaled output of AOGCMs and low precision in computational cells, uncertainty analysis is one of the principles in doing hydrological studies. For this reason, it is tried that investigati...