A probability density function theorem for the modulo y values of the sum of two statistically independent processes

1 January 1968

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE

Vol. 56 (2) , 204-205
https://doi.org/10.1109/proc.1968.6228

Abstract

It is demonstrated that when any process α(t) (random or deterministic) is added to a random process φ(t), where φ(t), modulo y, is uniformly distributed and statistically independent of α(t), the resultant random process, modulo y, is also uniformly distributed. The process α(t) need not be independent of φ(t).

Keywords

PROBABILITY DENSITY FUNCTION
RANDOM VARIABLES
DENSITY FUNCTIONAL THEORY
SIGNAL PROCESSING
RANDOM PROCESSES
STATISTICAL ANALYSIS
COMMUNICATION SYSTEMS
PHASE NOISE
VITERBI ALGORITHM

This publication has 2 references indexed in Scilit:

Phase-locked loop dynamics in the presence of noise by Fokker-Planck techniques
Proceedings of the IEEE, 1963
A threshold criterion for phase-lock demodulation
Proceedings of the IEEE, 1963