Digital synthesis of correlated stationary noise

Abstract

In this note we propose a method of generating stationary noise with a prescribed auto-covariance function by digital methods. The need for such a technique often arises in testing the performance of data processing and engineering systems, where inputs corrupted with correlated noise (of a known form) are required. The technique is quite simple and produces strict-sense stationary noise which agrees approximately with R ( τ ), the prescribed auto-covariance function (acf), over an interval [- T 0 , T 0 ]. The method consists of approximating the spectral density by a periodic process with spectral lines, and then synthesizing the periodic noise with random phases and appropriate amplitudes. In order to simplify discussion of the statistical properties of the noise generated, the technique is first presented in terms of exact harmonic analysis. In practice, discrete harmonic analysis as presented in the third section is used.