Digital Signal Processing and Applications with the OMAP-L138 eXperimenter

Chapter 6

Adaptive Filters

• Adaptive filter configurations
• Linear adaptive filters
• The least mean squares (LMS) algorithm
• Programming examples using C

6.1 INTRODUCTION

Adaptive filters are used in situations where the characteristics or statistical properties of the signals involved are either unknown or time-varying. Typically, a nonadaptive FIR or IIR filter is designed with reference to particular signal characteristics. But if the signal characteristics encountered by such a filter are not those for which it was specifically designed, then its performance may be suboptimal. The coefficients of an adaptive filter are adjusted in such a way that its performance according to some measure improves with time and approaches optimum performance. Thus, an adaptive filter can be very useful either when there is uncertainty about the characteristics of a signal or when these characteristics are time-varying.

Adaptive systems have the potential to outperform nonadaptive systems. However, they are, by definition, nonlinear and more difficult to analyze than linear, time-invariant systems. This chapter is concerned with linear adaptive systems, that is, systems that, when adaptation is inhibited, have linear characteristics. More specifically, the filters considered here are adaptive FIR filters.

At the heart of the adaptive systems considered in this chapter is the structure shown in block diagram form in Figure 6.1.

Its component parts are an adjustable filter, a mechanism for performance ...