The gamma-filter-a new class of adaptive IIR filters with restricted feedback

In this paper we introduce the generalized feedforward filter, a new class of adaptive filters that combine attractive properties of Finite Impulse Response (FIR) filters with some of the power of Infinite Impulse Response (IIR) filters. A particular case, the adaptive gamma filter, generalizes Widrow’s adaptive linear combiner (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and LMS adaptation is of the same computational complexity as the conventional adaline structure. Preliminary results indicate that the adaptive gamma filter is more efficient than adaline in terms of minimum mean square error. We extend the Wiener-Hopf equation to the gamma filter and develop some analysis tools.