New bounds for the variation of mean-square-continuous wide-sense-stationary processes

摘要

New bounds for real, continuous, nonnegative-definite functions are established. As an application it is shown that the variation of a real mean-square-continuous (MSC) wide-sense-stationary (WSS) process is bounded by its Maclaurin polynomials, either from below or from above depending on their degree. The least upper bound for the variation of a real MSC WSS process which depends solely on the process' spectral spread is also obtained. In comparison to previously published results, the new bounds present many advantages which are discussed. The extension of these bounds to complex MSC WSS processes is straightforward.