Bounds on moments for band-limited signals

Abstract

Presents a series of upper bounds on the first, second and third order moments of signals. These bounds as useful in practice in a variety of situations in which an estimate of the performance of the functions of the signals is required. The bounds are derived by constructing positive functions or by making use of the Holder inequalities for different choices of the p and q parameters. The theoretical context in which such bounds are developed and the indication as to how future bounds may conceivably be developed by using these techniques, is analysed. The methodology thus developed is applied to the determination of bounds for both continuous signals and discrete signals and it is shown there that the bounds for the corresponding cases can conceivably be vastly different, and the two cases appear to be converging only when the sampling frequency tends to infinity.<>