Applications of Adaptive Filters
Two possible application scenarios of adaptive filters are given
in fig. 3, system
identification and inverse filtering. For system identification the
adaptive filter is used to approximate an unknown system. Both the
unknown system and the adaptive filter are driven by the same input
signal and the adaptive filter coefficients are adjusted in a way,
that the output signal resembles the output of the unknown system,
i.e., the adaptive filter is used to approximate the unknown
system.
For inverse modeling or equalization the adaptive filter is used
in series with the unknown system and the learning algorithm tries
to compensate the influence of the unknown system on the test
signal by
minimizing the (squared) difference between the adaptive filters
output and the delayed test signal.
Figure 3: Two applications
of adaptive filters: System identification (left) and inverse
modeling/equalization (right)

Applications of adaptive filters further include the adaptive
prediction of a signal, used for example in ADPCM^{4} audio coding, adaptive noise or echo
cancellation, and adaptive beamforming (shaping of the
acoustic/radio `beam' transmitted/received by an array of
loudspeakers/microphones/antennas).
