SP - 8572 System Reconstruction From Higher - Order SpectraSlices

We consider the problem of system reconstruction from higher-order spectra (HOS) slices. We establish that the impulse response of a complex system can be reconstructed up to a scalar and a circular shift based on any pair of HOS slices, as long as the distance between the two slices satisses a certain condition. One slice is suucient for the reconstruction in the case of a real system. We propose a cepstrum based method for system reconstruction. We also propose a new method for the reconstruction of the system Fourier phase based on the phase of any odd-indexed bispectrum slice. Being able to choose the slices to be used in the reconstruction allows us to avoid bispectrum regions dominated by noise and reduce computational complexity.