Bispectrum modelling using quadratic filters

The bispectrum modelling problem using linear or quadratic filters is investigated. In the linear case, the third-order cumulant function C₃ of the output of a finite impulse response filter, driven by a white noise, is zero outside a finite domain. It is proven that this property is still valid if the filter is quadratic. The inverse problem is also considered. It is shown that, if the function C₃ is zero outside a finite domain, then the impulse response is necessarily finite in the linear case and may or may not be finite in the quadratic case. It is proven that every factorizable bispectrum can also be modeled with a quadratic filter, and an example to establish that the converse is false is given