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Power spectra of random spike fields and related processes

  • Pierre Brémaud (a1), Laurent Massoulié (a2) and Andrea Ridolfi (a3)
Abstract

In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

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Copyright
Corresponding author
Postal address: INRIA-ENS, Département d' Informatique, École Normale Supérieure, 45 rue d'Ulm, F-75005 Paris, France. Email address: pierre.bremaud@ens.fr
∗∗ Postal address: Microsoft Research, 7 J. J. Thomson Avenue, Cambridge CB3 0FB, UK.
∗∗∗ Postal address: School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
References
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Advances in Applied Probability
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