Adaptive IIR filtering and chaotic dynamics: application to audiofrequency coding

The authors study the chaotic dynamic associated with signal processing applications such as digital coding of audiofrequency signals, in which the real-time processing requirements are severe, due to the high speed input flow and low cost/complexity hardware. In the presence of narrowband signals the simple and robust least-mean-square adaptation of the autoregressive moving average predictor used in such systems creates local instabilities, but keeps global stability without external stability constraints, due to the self-stabilization phenomenon. The adaptation speed β is a bifurcation parameter that changes the predictor´s qualitative behavior. The route to chaos is illustrated by β increasing with typical period doublings and triplings, and the advent of a strange attractor. It is noted that in a real system, the accumulation of computation errors yields pseudochaotic effects and transient chaotic periods. This emphasizes the difference between the mathematical and experimental ideas of chaos