A mathematical framework to describe interpolated adaptive volterra filters

The major drawback for using adaptive Volterra filters in practical applications is the large number of adaptive filter weights required. Many research works can be found in the open literature aiming at reducing the computational burden of Volterra filters. Within this group, interpolated structures also have the purpose of reducing the computational overload. Such structures have been presented in an ad hoc manner in previous works. This paper proposes a formal mathematical framework to describe such a class of simplified adaptive Volterra filters. In addition, new insights on such structures are presented leading to a better understanding on interpolated adaptive Volterra filters. Numerical simulations are shown aiming to assess the performance of these computationally less-demanding structures of implementation.