A novel approach to introducing adaptive filters based on the LMS algorithm and its variants

This paper presents a new approach to introducing adaptive filters based on the least-mean-square (LMS) algorithm and its variants in an undergraduate course on digital signal processing. Unlike other filters currently taught to undergraduate students, these filters are nonlinear and time variant. This proposal introduces adaptive filtering in the context of a linear time-invariant system using a real problem. In this way, introducing adaptive filters using concepts already familiar to the students motivates their interest through practical application. The key point for this simplification is that the input to the filter is constant so that the adaptive filter becomes linear. Therefore, a complete arsenal of mathematical tools, already known by the students, is available to analyze the performance of the filters and obtain the key parameters to adaptive filters, e.g., speed of convergence and stability. Several variants of the basic LMS algorithm are described the same way.