This tutorial discusses three recent trends in adaptive filtering in view of the increased degrees of mobility and complexity in modern applications. One trend relates to a shift in emphasis from the design of adaptive filters to the design of interactive adaptive blocks within complex systems. A second trend relates to the need to endow adaptive filters with more complex learning mechanisms that can extract, digest and exploit any information about the surrounding environment. And a third trend relates to the need to characterize more fully the limits of performance of existing schemes and to develop variants that can meet more stringent specifications.

(a) From Adaptive Filters to Adaptive Systems. As is well-known, adaptive filters are devices that adjust their internal structure in response to changes in the surrounding environment. In this way, adaptive filters are endowed with both learning and tracking abilities that make them extremely useful in a variety of areas ranging from biomedical engineering, to consumer products, to communications, and also military electronics. In recent years, the explosive interest in these areas, and in information technology, has motivated heightened research in the field of adaptive filtering. In particular, in many applied problems of wide interest, emphasis is being placed on the analysis and design of interactive adaptive blocks within complex systems. In other words, emphasis is shifting from the design of adaptive filters to the design of adaptive systems.

(b) Model-Dependent Adaptive Filters. In addition, adaptive filters have long been well-known to be model-independent solutions. That is, their design rarely exploits prior knowledge about the environment. This fact is usually regarded as a strength: the filter worries about signal variations, not much the designer. However, model-independency is now becoming a burden. This is because the interest in communications and information technologies, including applications in wireless networks, voice over IP, HDTV, DSL, echo cancellation, home-phone networking, and channel equalization, has put forward a variety of new challenges as a result of the higher degrees of mobility and portability in communications systems. It is becoming almost self-evident that adaptive filters need to take in and digest any available prior information about the underlying signals and environment in order to provide superior performance. These challenges have also motivated heightened interest in understanding the limits of performance of exiting schemes and of developing variants that meet more stringent specifications.

(c) Performance Evaluation. The performance of an adaptive filter is usually evaluated in terms of its transient behavior and its steady-state behavior. The former provides information about how fast a filter learns, while the latter provides information about how well a filter learns. Such performance analyses are challenging in general since adaptive filters are, by design, time-variant and nonlinear stochastic systems. For this reason, it has been common in the literature to study different adaptive schemes separately due the differences that exist in their (nonlinear) update equations. However, it will be seen that by relying on energy arguments, one can develop a unifying framework for studying adaptation across different classes of filters and irrespective of input signal distributions. Not only that, but the energy arguments also provide a better understanding of the learning abilities of adaptive filters.

(d) Applications. Several examples of recent interest are discussed from the areas of wireless location finding, data conversion and source coding, human-machine interfaces and wearable computing, and space-time coded multi-user communications. In all these applications, adaptation and exploitation of model and data dependencies play a crucial role. In all, the tutorial is meant to provide the participant with an overview of recent developments in the field of adaptive filtering. In so doing, the tutorial will hopefully arm the participant with tools that can prove useful in the analysis and design of adaptive structures in a variety of more demanding contexts.