Simplified analysis of the LMS adaptive filter using a transfer function approximation

A simple approximation to the behavior of the LMS adaptive filter as a discrete transfer function is developed. This representation is a valid description for both deterministic inputs and for the expected results with random inputs (including correlated inputs). The results are shown to be exact for some classes of input including periodic signals. One result of this analysis is the demonstration that the LMS filter can produce results which are biased from the least-squares solution under the combined conditions of a nonzero mean primary and a correlated reference input.