Local Constraints Satisfied by Realizable Correlation Functions

摘要

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new, local constraints-each a consequence of the reciprocal-space non-negativity constraint-that are satisfied by the differentiable correlation functions.