Power Spectra of Random Spikes and Related Complex Signals

``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.

Autorentext

received his Ph.D. from EPFL (Switzerland) in 2004. His researchinterests and expertise are in the field of signal processing and stochasticmodeling for biomedicine, neurobiology, and communications. He iscurrently a senior R&D engineer at CSEM (Switzerland) and a lecturer at EPFL, where heteaches graduate courses.

Klappentext

``Random spikes'' belong to the common language used by engineers, physicists and biologists to describeevents associated with time records and locations in space. Data andsignals consisting of, or structured by, sequences of eventsare omnipresent in communications, neurobiology, computer science andsignal processing. We present a systematic study of theproperties of random spikes and related complex signals, the latterbeing the result of various operations (filtering, jittering,delaying, thinning, clustering, sampling, and modulating) on a basicevent stream. More specifically, we focus on second order properties,which are conveniently represented by the spectrum. The firstcontribution is theoretical: a modular approach for the constructionof complex signals and formulas for the computation of thespectrum that preserve such modularity (each additional featureadded to a basic model appears as an explicit separate contribution inthe corresponding basic spectrum). Applications of the theoretical results are then presented: spectralformulas for traffic analysis, randomly sampled signals, and pulse based communications, including UWB ones.