No abstract

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.

The work addresses the problem of approximating the sampled input-output (i/o) behavior of continuous-time nonlinear systems using discrete-time Volterra models. For an exactly band-limited nonlinear system for which a Volterra representation exists, the discrete-time Volterra model exactly corresponds to the sampled continuous-time Volterra kernels. Physical systems, as they are causal, are never exactly band-limited. Thus, a modeling error is introduced. By relaxing the causality condition and allowing a small processing delay, it is shown through simulation that more accurate discrete-time Volterra models compared to sampled continuous-time Volterra models can be generated.