The cross-bicepstrum: properties and applications for signal reconstruction and system identification

Complex cepstrum techniques are applied to cross-bispectra in order to simultaneously reconstruct three independent finite-time signals, given the cross-bispectrum of the three signals only. The method is applied to simultaneously identify three systems via the cross-bispectrum of their outputs, knowing only the statistics of the input. A least-squares method is presented to estimate the cross-bicepstral parameters of the three signals simultaneously. The method is nonparametric and noniterative, assuming only that the signals (or impulse responses) are exponential, stable, and have no zeros on the unit circle. It takes full advantage of the two-dimensional nature of the bispectrum to reconstruct the three signals (or identify the three systems) simultaneously