A note on the estimation of signal waveform

The problem of estimating signal waveform from received data that is corrupted by noise is briefly considered from the viewpoint of decision theory, in extension of some earlier work. The noise is assumed to be a Gauss process, which may or may not be stationary. Here, however, nothing is known about the signal process except that it may be deterministic, entirely random, or a mixed process. Two new features in the present application are the representation of the signal process as a linear expansion (M. S.) in complete orthonormal sets, and suitable choices of these sets. Examples involving discrete and continuous sampling on a finite interval, with various choices of a priori distributions of signal parameters are described, including calculations of Bayes and Minimax risks.