Title :
An analytical solution of the Fokker-Planck equation in the absence of noise
Author :
El-Masry, Ezz I.
Author_Institution :
University of Illinois, Urbana, IL
fDate :
5/1/1982 12:00:00 AM
Abstract :
A Fourier series with time varying coefficients is used to represent the modulo-2π phase error probability density function (pdf) in order to solve the Fokker-Planck (FP) equation as applied to the first-order phase-locked loop (PLL). The Fourier coefficients and hence the pdf are obtained analytically for the case when the initial phase error is a random variable uniformly distributed and the additive noise is zero.
Keywords :
Closed-form solution; Differential equations; Doppler shift; Fourier series; Frequency; Phase noise; Time series analysis; Time varying systems; Transmitters; Voltage-controlled oscillators;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/PROC.1982.12338
