On computing and implementing the running higher order statistics

The paper considers recursive bispectrum estimation using LTI filtering for time-average estimation of the third order cumulants. It is shown that by interchanging the order of time-average and Fourier transform, one of the filter poles can be first used to map the newly arrived time sample from the time-domain to the bispectrum-domain, The single pole-based recursive bispectrum estimate is then applied to the remaining filter singularities. The bispectrum estimate changes its characteristics as it is processed by each pole and zero. It is shown that cascade implementation of the time-averaging filter allows an easy access to distinct bispectrum estimators with different temporal-spectral resolution tradeoff. Systolic array implementation and simulations of the proposed form of recursive estimation are presented.<>