DocumentCode :
944327
Title :
The effect of instantaneous nonlinear devices on cross-correlation
Author :
Leipnik, Roy
Volume :
4
Issue :
2
fYear :
1958
fDate :
6/1/1958 12:00:00 AM
Firstpage :
73
Lastpage :
76
Abstract :
If 
are two noises (stochastic processes), 
and 
are functions describing the action of two instantaneous nonlinear devices, we say that the 
cross-correlation property holds in case the cross-correlation of 
with 
is proportional to the cross-correlation of 
with 
, whenever and are polynomials of degrees not exceeding 
and 
, respectively. We take 
or 
to mean that or is any continuous function. The Barrett-Lampard expansion 
of the second-order joint density of 
and is used to derive an expression for the cross-correlation of and . This expression yields necessary and sufficient conditions for the validity of the cross-correlation property in three cases: 
and 
stationary, 
unrestricted; stationary, unrestricted; stationary, 
. Examples are constructed with the help of special orthonormal polynomials illustrating the necessity and sufficiency of the conditions.
are two noises (stochastic processes), and are functions describing the action of two instantaneous nonlinear devices, we say that the cross-correlation property holds in case the cross-correlation of with is proportional to the cross-correlation of with , whenever and are polynomials of degrees not exceeding and , respectively. We take or to mean that or is any continuous function. The Barrett-Lampard expansion of the second-order joint density of and is used to derive an expression for the cross-correlation of and . This expression yields necessary and sufficient conditions for the validity of the cross-correlation property in three cases: and stationary, unrestricted; stationary, unrestricted; stationary, . Examples are constructed with the help of special orthonormal polynomials illustrating the necessity and sufficiency of the conditions.Keywords :
Correlation functions; Nonlinearities; Detectors; Gaussian processes; Information theory; Nonlinear distortion; Polynomials; Probability distribution; Random processes; Reactive power; Stochastic processes; Sufficient conditions; Terminology;
fLanguage :
English
Journal_Title :
Information Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-1000
Type :
jour
DOI :
10.1109/TIT.1958.1057445
Filename :
1057445
Link To Document :
