Title :
Transitional process of RC circuit and LMS algorithm
Author :
Pei, Bingnan ; Li, Chuanguang
Author_Institution :
Dept. of Electron. Eng., Zhengzhou Univ., Henan, China
Abstract :
The eigenvector approach in matrix theory is used to study a stochastic differential equation whose resolution corresponds with that of the least mean square (LMS) algorithm, based on Ljung´s (1977) stochastic theory. A conclusion comes from our study that the trace of the weight adjustment of the algorithm is, in statistics, the same as the transitional process of an RC circuit of first order. As a result, the device designed with the algorithm has the same properties as a parallel filtering array which consists of some RC circuits of first order has. A relationship between the cut-off frequency of an adaptive system and the eigenvalues (power components) as well as band width of a signal is highlighted
Keywords :
RC circuits; circuit theory; difference equations; eigenvalues and eigenfunctions; least mean squares methods; matrix algebra; signal resolution; stochastic processes; LMS algorithm; RC circuit; adaptive system; eigenvector approach; least mean square algorithm; matrix theory; parallel filtering array; resolution; stochastic differential equation; stochastic theory; transitional process; weight adjustment; Adaptive systems; Algorithm design and analysis; Circuits; Cutoff frequency; Differential equations; Eigenvalues and eigenfunctions; Filtering algorithms; Least squares approximation; Statistics; Stochastic processes;
Conference_Titel :
Signal Processing, 1996., 3rd International Conference on
Conference_Location :
Beijing
Print_ISBN :
0-7803-2912-0
DOI :
10.1109/ICSIGP.1996.571188
