On probability distributions for filtered white noise
- 1 July 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 13 (3) , 481-484
- https://doi.org/10.1109/TIT.1967.1054029
Abstract
When white noise generated by an underlying Poisson process is filtered by any member of a large class of stable (not necessarily linear nor stationary) filters, the first-order probability distributions of the filter output is infinitely divisible. The Kolmogorov canonical form for the characteristic function is displayed and related to the parameters of the white noise and of the filter. In certain linear stationary cases, cubclasses of the infinitely divisible distributions are identified. An invariance property of the bilateral exponential distribution is demonstrated.Keywords
This publication has 8 references indexed in Scilit:
- The effect of autoregressive dependence on a nonparametric test (Corresp.)IEEE Transactions on Information Theory, 1967
- An isospectral family of random processesIEEE Transactions on Information Theory, 1960
- Amplitude Distribution of Shot NoiseBell System Technical Journal, 1960
- On stochastic processes connected with certain physical recording apparatusesActa Mathematica Hungarica, 1955
- On secondary processes generated by a Poisson process and their applications in physicsActa Mathematica Hungarica, 1954
- On the Theory of Random Noise. Phenomenological Models. IJournal of Applied Physics, 1951
- Mathematical Analysis of Random NoiseBell System Technical Journal, 1944
- Statistical Analysis of Certain Types of Random FunctionsThe Annals of Mathematical Statistics, 1944