Abstract: We present a new approach using vector space base functions to discuss the adaptive ⅡR filter with restricted feedback——Gamma filter and Laguerre filter, and propose a unified model for them. We analyze and compare this class of filters in detail, showing that Gamma filter has advantages over Laguerre filter. We also derive the Wiener-Hopf equation and the corresponding LMS algorithm of them. Some simulation results are also presented.

Key words: adaptive IIR filter, base functions, Laguerre filter, vector space, Gamma filter