Polyphase Representation of Multirate Nonlinear Filters and Its Applications

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper proposes a polyphase representation for nonlinear filters, especially for Volterra filters. To derive the new realizations the well-known linear polyphase theory is extended to the nonlinear case. Both the upsampling and downsampling cases are considered. As in the linear case (finite-impulse response filters), neither the input signal nor the Volterra kernels must fulfill constraints in order to be realized in polyphase form. The computational complexity can be reduced significantly because of two reasons. On the one hand, all operations are performed at the low sampling rate and, on the other hand, a new null identity allows to remove many coefficients in the polyphase representation. Furthermore, some applications involving a nonlinear filter, an upsampler, and/or a downsampler are discussed to demonstrate the utility of the new approach to multirate nonlinear signal processing. </para>