Chapter 11

Deterministic filters are implemented in linear and time-invariant systems to remove out-of-band noise or unwanted signals. When the unwanted signals are known in terms of their frequency band, a system can be designed that does not require any adaptation in real time. In contrast, there are many scenarios where the system cannot be deterministically determined and is also time-variant. Then the system is designed as a linear time-invariant (LTI) filter in real time and, to cater for time variance, the filter has to update the coefficients periodically using an adaptive algorithm. Such an algorithm uses some error-minimization criterion whereby the output is compared with the desired result to compute an error signal. The algorithm adapts or modifies the coefficients of the filter such that the adapted system generates an output signal that converges to the desired signal.

There are many techniques for adaptation. The selection of an algorithm for a particular application is based on many factors, such as complexity, convergence time, robustness to noise, ability to track rapid variations, and so on. The algorithm structure for effective implementation in hardware is another major design consideration.