System identification using polycepstra with interpolation

This paper extends the cepstral calculus based on our novel approach with the frequency-domain interpolation to a multidimensional case. The derived differential polycepstra may be implemented successfully to the system identification even when the system input is excited by symmetrically distributed i.i.d. random noise. We show that the differential polycepstrum of any order shrinks to a one-dimensional differential cepstrum located in two identical replicas, on the x-axis and the main diagonal of the multidimensional cepstral space, if we process the system output signal whose excitation was i.i.d. random white noise. The interpolation-based calculation asymptotically eliminates cepstral aliasing and overlapping of the causal and anticausal part of differential cepstrum. At the same time, the complexity of the computational algorithm is lower compared to the techniques of cepstral aliasing reduction. We reveal this newly derived computational algorithm and depict its strength on identification of two simulated system responses