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

Abstract

A method is proposed for the efficient implementation of a class of second-order Volterra filters where their quadratic kernels are recursively constructed from a set of isotropic subkernels (ISKs). The quadratic kernel of this class of filters can be factorised into a diagonal form by a Walsh-Hadamard transform (WHT) and be implemented using a transform-and-multiply structure. An algorithm for determining the quadratic ISK kernel for the nonlinear prediction of speech signals is presented.