Modeling arbitrary polynomial bispectra in one and two dimensions

The authors propose a novel model, called a system with multiplicity (SWM), which is a refinement of the model proposed by Sakaguchi and Sakai (1989), to represent arbitrary polynomial bispectra. It is shown that an arbitrary polynomial bispectrum of a 1-D signal can always be realized using an SWM with FIR (finite impulse response) components. An algorithm is then developed for the identification of SWM that will match a given polynomial bispectrum. The authors address the problem of simultaneously matching an arbitrary polynomial bispectrum and a rational power spectrum function using an SWM. It is shown 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. It is shown that in two dimensions an arbitrary polynomial bispectrum cannot always be uniquely modeled using an SWM with 2-D FIR components having different extents