Recursive and least-squares methods for reconstructing the impulse response of a nonminimum phase, linear time-invariant (NMP-LTI) MA system from its (k+1)st-order spectrum (k<1) are presented. The methods are nonparametric. They are based on computing the complex cepstrum of the impulse response sequences of the unknown system from the diagonal slice of the (k+1)st-order spectrum. The computational complexity of the system identification problem can be considerably reduced by using slices of higher-order spectra.
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