The effects of precision on the fast, recursive least-squares transversal filters for adaptive filtering

Fast Recursive Least-Squares Transversal Filters (FTF), an important class of algorithms for adaptive filtering, have the well known problem of numerical instability. Several recent papers have suggested methods to modify the algorithm presented by Cioffi [3] to improve the algorithm’s stability. This paper explores the relationship between precision and stability of the adaptive filter. The effect of changing the adaptive time constant and the filter order are also investigated. These effects are studied for a floating point implementation of the FTF filter that allows for limiting the number of bits used in the mantissa of the results of all additions and multiplications.