Nonlinear Digital Filters Analysis and Application
and electronic engineering. They are widely employed in signal processing,
communications, control, circuits design, electrical engineering and biomedi-cal engineering communities. However, as digital filters are linear time invariant
systems, any nonlinear behaviors occur in digital filters should be avoided. The
first observed nonlinear phenomenon was the limit cycle behavior discovered
in 1965 by implementing a digital filter via a finite state machine. Since then,
engineers have tried to avoid the occurrence of the limit cycle behavior. In 1988,
L. O. Chua and T. Lin (Chaos in Digital Filters, IEEE Transactions on Circuits
and Systems, Vol. 35, no. 6, pp. 648–658) observed that besides the occurrence
of the limit cycle behavior, digital filter may exhibit fractal behaviors if imple-mented via the two’s complement arithmetic. This observation implies that
digital filters associated with nonlinearities may exhibit chaotic behaviors and
this property may be utilized in some applications. While avoiding the occur-rence of nonlinear behaviors, engineers began investigating the applications of
digital filters with nonlinearities and found that many applications – such as
computer cryptography – secure communications, etc. Hence, the subject of
nonlinear digital filters plays an increasingly important role in electrical and
electronic engineering.
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