Zy. Ren et H. Schutze, A STABILIZED FAST TRANSVERSAL FILTERS ALGORITHM FOR RECURSIVE LEAST-SQUARES ADAPTIVE FILTERING, Signal processing, 39(3), 1994, pp. 235-246
In this paper, the numerical stability of the well known gain-normaliz
ed fast transversal filters (GFTF) algorithm is analytically investiga
ted. Starting from an analysis of the error propagation, suitable roun
d-off errors difference equations (REDE) are derived. The stabilizatio
n of the GFTF algorithm can be achieved by stabilizing the REDE. The r
esulting algorithm is numerically stable, having only 7N + 27 multipli
cations and divisions per recursion (MADPR). The numerical stability o
f the proposed algorithm is demonstrated by the simulation results.