Limited-precision effects in adaptive filtering

The effects of limited-precision errors in several popular adaptive-filtering algorithms are analyzed. Performance degradations caused by limited-precision quantization of internal algorithmic quantities are often found to be much larger than what might be otherwise expected. Furthermore, in many cases, limited-precision errors are found to accumulate in time without bound, leading to an eventual overflow. This overflow is an unacceptable phenomenon in practice. Where possible, we list modifications to the infinite-precision design criteria which prevent the overflow at the expense of a small degradation from the performance that is achievable in infinite precision. We also delineate unacceptable numerical problems in some of the adaptive filtering algorithms for which no solution is yet ubiquitously accepted or useful. Stochastic gradient (LMS), recursive least squares (RLS), and frequencydomain methods are all discussed. As such, this paper contains a mixture of tutorial and novel material in an effort to assist the reader in the limited-precision implementation of an adaptive-filtering algorithm.