TUTORIAL ON HIGHER-ORDER STATISTICS (SPECTRA) IN SIGNAL-PROCESSING AND SYSTEM-THEORY - THEORETICAL RESULTS AND SOME APPLICATIONS

During the past few years there has been an increasing interest in applying higher-order statistics to a wide range of signal processing and system theory problems. These statistics are very useful in problems where either non-Gaussianity, nonminimum phase, colored noise, or nonlinearities are important and must be accounted for. More than 200 papers have already been published. These papers contain both theoretical and algorithmic results. The purpose of the present tutorial paper is twofold, namely: 1) to collect what this author believes to be some of the most useful theoretical results in one place (they are presently scattered in many papers), thereby making them readily accessible to readers for the first time (derivations are provided in the Appendix for many of the results), and, 2) to describe the applications of higher-order statistics to the identification of (possibly) nonminimum phase channels from just noisy output measurements. More than 20 new methods are summarized for the latter.