LINEAR MAPPINGS OF CROSS-SPECTRAL DENSITY ONTO GENERALIZED RADIANCE

A class of generalized radiances characterized by filter functions was recently introduced into the statistical wave theory via the phase-sp ace representations of the cross-spectral density operator. It is show n that if the generalized radiances are represented as linear transfor mations of the cross-spectral density, there exists a unique correspon dence between the filter functions and the transform kernels within ce rtain galilean invariant transformations. Explicit expressions are der ived for this correspondence, and the radiometric meanings of the cons traints placed on the phase-space filter functions are elucidated.