The Open Signal Processing Journal

2010, 3 : 1-5
Published online 2010 January 19. DOI: 10.2174/18768253010030100001
Publisher ID: TOSIGPJ-3-1

The Trapezoidal Method of Steepest-Descent and its Application to Adaptive Filtering

T. J. Moir
School of Engineering and Advanced Technology, Massey University at Albany, Auckland, New-Zealand.

ABSTRACT

The method of steepest-descent is re-visited in continuous time. It is shown that the continuous time version is a vector differential equation the solution of which is found by integration. Since numerical integration has many forms, we show an alternative to the conventional solution by using a Trapezoidal integration solution. This in turn gives a slightly modified least-mean squares (LMS) algorithm.

Keywords:

Steepest-Descent, Least-mean squares (LMS), Adaptive filters.