Statistical-mechanical analysis of adaptive filter with clipping
In most practical adaptive signal processing systems, e.g., active noise
control, active vibration control, and acoustic echo cancellation,
substantial nonlinearities that cannot be neglected exist. In this
paper, we analyze the behaviors of an adaptive system in which the
output of the adaptive filter has the clipping saturation-type
nonlinearity by a statistical-mechanical method. We discuss the
dynamical and steady-state behaviors of the adaptive system by
asymptotic analysis, steady-state analysis, and numerical calculation.
As a result, it has become clear that the saturation value has the
critical point at which the system’s mean-square stability and
instability switch. The obtained theory well explains the strange
behaviors around the critical point observed in the computer simulation.
Finally, the exact value of the critical point is also derived.