MODELING ARBITRARY POLYNOMIAL BISPECTRA IN ONE AND 2 DIMENSIONS

It is well known that an arbitrary bispectrum in the form of a polynom ial cannot always be realized by a white noise driven finite impulse r esponse (FIR) linear, shift-invariant (LSI) system. In this paper, we first propose a new model, called a system with multiplicity (SWM), wh ich is a refinement of the model proposed by Sakaguchi et al., to repr esent arbitrary polynomial bispectra. It is shown that an arbitrary po lynomial bispectrum of a one-dimensional (1-D) signal can always be re alized using an SWM with FIR components. An algorithm is then develope d for the identification of SWM that will match a given polynomial bis pectrum. We then address the problem of simultaneously matching an arb itrary polynomial bispectrum and a rational power spectrum function us ing an SWM. We show that this can always be accomplished by including another LSI component that is driven by a Gaussian input to the system . Experimental results for matching an estimated bispectrum as well as simultaneously matching a polynomial bispectrum and a power spectrum of some 1-D signals are presented. Finally, we show that in two dimens ions (2-D) an arbitrary polynomial bispectrum cannot always be uniquel y modeled using an SWM with 2-D FIR components having different extent s.