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 ADPCM⁴ audio coding, adaptive noise or echo cancellation, and adaptive beam-forming (shaping of the acoustic/radio `beam' transmitted/received by an array of loudspeakers/microphones/antennas).