Kód: 06823063
``Random spikes'''' belong to the common language used by §engineers, physicists and biologists to describe§events associated §with time records and locations in space. Data and§signals §consisting of, or structured by, sequences ... celý popis
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``Random spikes'''' belong to the common language used by §engineers, physicists and biologists to describe§events associated §with time records and locations in space. Data and§signals §consisting of, or structured by, sequences of events§are omnipresent in communications, neurobiology, computer science and§signal §processing. We present a systematic study of the§properties of §random spikes and related complex signals, the latter§being the §result of various operations (filtering, jittering,§delaying, thinning, §clustering, sampling, and modulating) on a basic§event stream. More §specifically, we focus on second order properties,§which are §conveniently represented by the spectrum. The first§contribution is §theoretical: a modular approach for the construction§of complex §signals and formulas for the computation of the§spectrum that §preserve such modularity (each additional feature§added to a basic §model appears as an explicit separate contribution in§the §corresponding basic spectrum). Applications of the §theoretical results are then presented: spectral§formulas for traffic §analysis, randomly sampled signals, and pulse based §communications, including UWB ones.
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