System reconstruction based on selected regions of discretized higher order spectra

We consider the problem of system reconstruction from arbitrarily selected slices of the nth-order output spectrum. We establish that unique identific ation of the impulse response of a system can be performed, up to a scaler and a circular shift, based on any two one-dimensional (I-D) slices of the discretized nth-order output spectrum, (n greater than or equal to 3), as l ong as the distance between the slices and the grid size satisfy a simple c ondition. For the special case of real systems, one slice suffices for syst em reconstruction. The ability to choose the slices to be used for reconstr uction enables us to avoid regions of the nth-order spectrum, where the est imation variance is high, or where the ideal polyspectrum is expected to be zero, as is the case for bandlimited systems. We show that the obtained sy stem estimates are asymptotically unbiased and consistent. We propose a mec hanism for selecting slices that result in improved system estimates. We al so 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.