Quadratic filters for signal processing: principles and applications

An overview of the principles of quadratic filtering and its applications to the processing of 1-D and M-D signals is presented. Two vector notations are introduced to simplify the expressions of the Volterra kernels, and two corresponding efficient realizations are suggested for finite-support 1-D and M-D quadratic filters. Both realizations exhibit properties of modularity and regularity very suitable for VLSI implementations and permit computational and hardware advantages. The linearity of the output of Volterra filters with respect to the kernel elements allows the extension of the theory of the optimum linear filter to the optimum nonlinear Volterra filter, according to the minimum mean-square error criterion.<>