Spectral dispersion of modulated signals due to oscillator phase instability  White and random walk phase model
Abstract
This paper considers the modeling of oscillator phase instability and the resulting spectral dispersion. A phase covariance matrix method is developed for determining the autocorrelation function and the power spectral density of the oscillator sinusoidal RF signal when corrupted by a superposition of a white phase random process and a random walk phase random process. By limiting the discussion to phase covariance matrices, it is shown that the direct use of a certain class of nonstationary phase random processes leads to stationary RF signal autocorrelation functions and associated power spectral densities. This is so despite the nonstationary phase driving force. The procedures provided here are also applied towards the determination of the average autocorrelation function and the average spectrum when the cisoidal oscillator signal undergoes modulation. Modulating waveforms used as examples include the CW, the infinite pulse train, and the finite pulse train.
 Publication:

NASA STI/Recon Technical Report A
 Pub Date:
 July 1983
 Bibcode:
 1983STIA...8340922V
 Keywords:

 Frequency Stability;
 Harmonic Oscillators;
 Phase Shift;
 Random Processes;
 Signal Analysis;
 Wave Dispersion;
 Autocorrelation;
 Covariance;
 Mathematical Models;
 Modulation;
 Power Spectra;
 Random Walk;
 Waveforms;
 Electronics and Electrical Engineering