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Using a pair of HOS slices for system reconstruction: methodology and performance analysis

We present a method for unique identification of the impulse response of a system, based on any two horizontal slices of the discretized n-th order output spectrum, (n/spl ges/3). We establish a necessary and sufficient condition for the relationship between the distance of the slices and the grid size, under which reconstruction is possible. The conducted statistical analysis of the method indicates that, if the n-th order spectrum estimates are asymptotically unbiased and consistent, the system estimates are asymptotically unbiased and consistent too. 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 finally 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.