Correlation Function and Spectral Density

Real random processes (stochastic processes) exhibit unpredictable changes with time and defy precise prediction. Practically, it is not possible to determine the probability distribution function of these real random processes. Then it is important to describe partially the mean, the correlation function and the covariance function of these real random processes which is defined by stationary processes or Ergodic processes. The collection of all possible recording of these processes, is called an ensemble. The ensemble correlation functions play an important role in the design of the correlation receiver and the matched filter receiver. The correlation function studies the statistically dependent and independent relation between two real random processes. The correlation function is independent of the time and depends only on the time difference (delay).

Keywords: Autocorrelation function, Cross-Correlation function, Energy signals, Power signals.