"Whiter than white" noise

Abstract

This paper brings together two strands of current interest in signal processing. While second order techniques and minimum variance criteria are well understood, there is a growing requirement to study the performance criteria that involve higher order statistics in order to evaluate deviation from Gaussianity, linearity and stationarity of observed data. There is a complimentary requirement for the generation of random test sequences which have prescribed (or minimal) higher order statistics, to facilitate the analysis of systems in order to determine linearity/non-linearity, time invariance vs time varying parameters. This paper proposes a new method for minimising the third order cumulant spread of random sequences with symmetric pdf, and provides a closed form solution for the weightings required to achieve this. Numerous computed results are included to verify performance.<>