Proper complex random processes with applications to information theory

摘要: The covariance of complex random variables and processes, when defined consistently with the corresponding notion for real variables, is shown to be determined by usual together a quantity called pseudo-covariance. A characterization uncorrelatedness wide-sense stationarity in terms pseudo-covariance given. Complex processes vanishing are proper. It that properness preserved under affine transformations complex-multivariate Gaussian density assumes natural form only proper variables. maximum-entropy theorem generalized case. differential entropy vector fixed correlation matrix maximum if proper, Gaussian, zero-mean. circular introduced. For class discrete Fourier transform correspondence derived relating time domain frequency domain. An application theory presented. >