Blind reconstruction of non-minimum-phase systems from 1-D oblique slices of bispectrum

The author considers the problem of identifying a non-minimum-phase signal from one-dimensional slices of its output bispectra. It is proved that any single slice of the bispectrum carries sufficient information to estimate the impulse response of a complex valued system within a time shift, as long as the chosen slice is not parallel to any one of the frequency axes or to the diagonal at 135 degrees. The author also derives identifiability criteria associated with complex-valued signals that admit finite-dimensional ARMA representations. One-dimensional techniques are proposed for signal reconstruction from bispectrum slices and their performance is investigated through Monte-Carlo simulations. The slices required for the proposed method can be estimated on a polar raster directly from observations, avoiding the heavy computational burden associated with cumulant estimates. The freedom to choose arbitrarily oriented and shifted slice(s) allows bispectrum regions dominated by larger estimation variance and higher noise to be avoided.