Correlation Functions, Spectral Power Densities of Random Signals

Abstract

We first study in this chapter the properties of digital random signals. We encounter two functions which are fundamental for signal analysis: the correlation function and the power spectral density (PSD) defined for wide sense stationary (WSS) random signals. The PSD is defined as the Fourier transform of the correlation function. We study the filtering of WSS signals by LTI systems, and give the theorems linking correlations and DSP of input and output signals. The coherence function, defined afterward, is a powerful tool to identify and quantify the sources constituting the noise in a noisy signal. At the end of this chapter, we give a brief definition of correlation functions and power spectral densities of analog signals. We study the influence of a filter for increasing the signal-to-noise ratio or matched filtering of a noisy signal with random noise. Exercises with solutions at the end of the chapter will help the reader to become familiar with the results.