Abstract
Nowadays, high order statistics (HOS) are used in many applications of signal processing. By HOS, we mean moments or cumulants of order higher than two in the time domain, and their multidimensional Fourier transform called polyspectrum in the frequency domain. In real-time applications, it can be useful to recursively estimate the cumulants. By using the ergodicity assumption, we develop in this paper a recursive formula 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-squares form of the C( Q, k) algorithm based on the use of this recursive formula for identifying FIR models. The performance of this LS- C( Q, k) algorithm is illustrated by some simulation results.
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