High speed adaptive signal progressing using the delta operator

In this paper the use of the delta operator, i.e., a scaled difference oper ator, in adaptive signal processing with fast sampling is presented. It is recognized that most discrete-time signals and systems are the result of sa mpling continuous-time signals and systems. When sampling is fast, all resu lting signals and systems tend to become ill conditioned and thus difficult to deal with using the conventional algorithms. The delta operator based a lgorithms, as will be developed in this paper, are numerically better behav ed under finite precision implementations for fast sampling. Therefore, the y provide many improvements in terms of numerical accuracy and/or convergen ce speed. Furthermore, the delta operator based algorithms can in most case s be shown to have meaningful continuous-time limits as the sampling become s faster and faster. Thus they function as a bridge in unifying discrete-ti me algorithms with continuous-time algorithms. This enhances our insight in to and overall understanding of these various algorithms. In this paper, se veral well-known algorithms in statistical and adaptive signal processing w ill be cast into their delta operator counterparts. Some new delta operator based algorithms will also be developed. Whenever applicable, correspondin g continuous-time limits of these delta operator based algorithms will be p ointed out. Computer simulation results using finite precision implementati on will also be presented for some of the new algorithms, which generally s how much improvement compared with the results from using traditional algor ithms. (C) 2000 Academic Press.