Mutual Information for Gaussian Processes

A new expression for average mutual information (AMI) of two Gaussian processes is obtained, extending earlier work of Gel’fand and Yaglom. This result is expressed in terms of the covariance and cross-covariance operators of the two processes, while the previous results were stated in terms of projection operators in random variable space. Relations are also obtained between the occurrence of finite or infinite AMI and nonsingular or singular detection for a Gaussian signal imbedded in additive Gaussian noise.