Nowadays, high order statistics (HOS) are used in many applications of
signal processing. By HOS, we mean moments or cumulants of order high
er than two in the time domain, and their multidimensional Fourier tra
nsform called polyspectrum in the frequency domain. In real-time appli
cations, it can be useful to recursively estimate the cumulants. By us
ing the ergodicity assumption, we develop in this paper a recursive fo
rmula for estimating the fourth-order cumulants of a real- or complex-
valued, zero mean, stationary scalar stochastic process. The behaviour
of this recursive estimator is illustrated in the cases of simulated
stationary and non-stationary processes. We also present a least-squar
es form of the C(Q,k) algorithm based on the use of this recursive for
mula for identifying FIR models. The performance of this LS-C(Q,k) alg
orithm is illustrated by some simulation results. (C) 1998 Published b
y Elsevier Science B.V. All rights reserved.