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Power-law shot noise and its relationship to long-memory α-stable processes

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3 Author(s)
A. P. Petropulu ; Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA ; J. -C. Pesquet ; Xueshi Yang

We consider the shot noise process, whose associated impulse response is a decaying power-law kernel of the form tβ/2-1 . We show that this power-law Poisson model gives rise to a process that, at each time instant, is an α-stable random variable if β<1. We show that although the process is not α-stable, pairs of its samples become jointly α-stable as the distance between them tends to infinity. It is known that for the case β>1, the power-law Poisson process has a power-law spectrum. We show that, although in the case β<1 the power spectrum does not exist, the process still exhibits long memory in a generalized sense. The power-law shot noise process appears in many applications in engineering and physics. The proposed results can be used to study such processes as well as to synthesize a random process with long-range dependence

Published in:

IEEE Transactions on Signal Processing  (Volume:48 ,  Issue: 7 )