Chaos in digital filters

It is shown that when the second-order digital filter is implemented using a two's-complement arithmetic for the addition operation, it can exhibit chaotic behavior for certain regions in the parameter space. The overflow nonlinearity of the adder results in a rather complex dynamics, with a phase portrait that is self-similar and has a fractal geometry. The intricate chaotic dynamics of this nonlinear filter is analyzed using symbolic dynamics involving three symbols.<>