Correlation and spectral analysis of nonlinear transformations of sequency-band-limited signals

This note considers the representation of sequency-band-limited random signals in time, sequeney, and frequency domains. Computationally convenient expressions for correlation functions and associated (frequency) power spectral densities are derived via corresponding sequency sampling expansions. The approach of obtaining correlation and spectral density functions via sequency sampling expansions is further employed in the analysis of nonlinear transformations of such signals. On the other hand, employing corresponding cardinal series expansions will generally render such computations as formidable tasks. Hence, the former approach may be deemed more advantageous, even under approximate conditions of sequency-band-limitedness.