Scheduled System Maintenance:
On May 6th, single article purchases and IEEE account management will be unavailable from 8:00 AM - 5:00 PM ET (12:00 - 21:00 UTC). We apologize for the inconvenience.
By Topic

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

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

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

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:

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