Discrete-time (or digital) filters are ubiquitous in todays
signal processing applications. Filters are used to achieve desired
spectral characteristics of a signal, to reject unwanted signals,
like noise or interferers, to reduce the bit rate in signal
The notion of making filters adaptive, i.e., to alter parameters
(coefficients) of a filter according to some algorithm, tackles the
problems that we might not in advance know, e.g., the
characteristics of the signal, or of the unwanted signal, or of a
systems influence on the signal that we like to compensate.
Adaptive filters can adjust to unknown environment, and even track
signal or system characteristics varying over time.