System reconstruction from selected HOS regions

System reconstruction from arbitrarily selected slices of the n-th order output spectrum is considered. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two horizontal slices of the discretized n-th order output spectrum, (n⩾3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice suffices for reconstruction. The ability to select the slices to be used for reconstruction enables one to avoid regions of the n-th order spectrum where the estimation variance is high, or where the ideal bispectrum is expected to be zero, as in the case of bandlimited systems. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the proposed method over existing approaches in the case of bandlimited systems