Bicepstrum computation based on second- and third-order statistics with applications

Abstract

The authors introduce a novel approach for bicepstrum (i.e. cepstrum of the bispectrum) estimation that combines the use of second- and third-order statistics, and show application of this method to the problem of detecting and estimating the time delay between signals received at two spatially separated sensors together with noise, as well as to nonminimum phase system identification. The approach for time delay estimation is parametric, in the sense that it provides the time delay estimates directly and explicitly instead of examining the results of some reference functions. The performance of this method is demonstrated for different noise conditions and lengths of data. The performance is also compared to that of the least-squares method, which is based entirely on second-order statistics. It is shown that bicepstrum-based time delay estimation provides larger performance gain when the noise sources are Gaussian spatially correlated with unknown correlation function. >