Multistage multirate adaptive filters

A procedure for the adaptation of multistage multirate filters is developed in the context of a system identification perspective. The system to be identified is the cascade of a multistage decimator followed by a multistage interpolator. For this structure, an identifiability condition is established which is sufficient to guarantee that the stagewise systems may be uniquely determined from input-output data in the ideal, exact model order case. An algorithm is then described that achieves exponential convergence of the system parameter estimates to their desired values given satisfaction of these identifiability conditions.