Phase-Locked Loop Operation in the Presence of Impulsive and Guassian Noise

A first-order phase-locked loop with detuning is considered in the presence of white Gaussian noise and random amplitude impulsive noise with Poisson times. The stochastic equation for the phase error density is of infinite order, but when the stationary mod-2π phase density is represented by a Fourier series, a linear second-order difference equation is the Fourier coefficients results. The difference equation is solved numerically, and the phase error density is generated from the Fourier series. This method uses no approximations and is valid for any impulsive amplitude probability density.