VOLTERRA FUNCTIONAL EXPANSION FOR THE LOGARITHM OF THE LIKELIHOOD RATIO FOR DETECTION OF A MEMORYLESS NON-LINEAR FUNCTIONAL OF A RANDOM PROCESS IN GAUSSIAN WHITE NOISE

A Volterra functional expansion for the logarithm of the likelihood ratio, for detection of a memoryless nonlinear functional of a random process in Gaussian white noise, is presented. For the special case of detection of a zero-mean Gaussian process in Gaussian white noise, it is shown that the Volterra expansion reduces to well-known results. An approximation to the Volterra expansion is suggested for some problems with periodic nonlinearities. © 1979, Acoustical Society of America. All rights reserved.