Adaptive recursive-least-squares and lattice transversal filters for continuous-time signal processing

The authors present lattice and transversal filters for adaptive recursive-least-squares (RLS) processing of continuous-time signals. They have the same structure as the discrete-time RLS adaptive lattice and transversal configurations, namely, a lattice cascade and a tapped-delay-line, respectively, but with continuously adjustable parameters that are updated by propagating a set of coupled differential equations. While the discrete-time scheme involves a fundamental unit of time (viz. the sampling period of the signal) that determines both the duration of the delay and the rate of gain-updating, the new continuous-time scheme involves a delay of arbitrary duration and continuously varying gains. It turns out that the conceptual and computational complexity of the continuous-time filters is less than for their discrete-time counterparts