Efficient implementation of a class of isotropic quadratic filters by using Walsh-Hadamard transform

An efficient method is proposed for the implementation of a class of second-order Volterra (quadratic) filters where their quadratic kernels are constructed from a set of isotropic sub-kernels (ISK). The quadratic kernel of this class of Volterra filters can be completely defined by N independent elements where N is the kernel dimension. It is shown that, due to the ISK structure of the filter, the kernel matrix can be factorized into a diagonal matrix by Walsh-Hadamard transform (WHT) and then implemented efficiently with a transform-and-multiply structure. An example on applying the proposed quadratic filter for nonlinear prediction of audio signals is given