Continuous-time lease-squares fast transversal filters

A recursive-least-squares (RLS) adaptive fast transversal filter (FTF) for processing of continuous-time signals is presented. It has the same structure as the discrete-time least-squares FTF, namely, a tapped-delay-line with time-varying gains, which are updated by propagating a set of coupled recursions. However, while the discrete-time scheme involves a fundamental unit of time (i.e., the sampling period of the signal), which determines both the duration of the delay and the rate of gain updating, our continuous-time scheme involves a delay of arbitrary duration and continuously-varying gains. Also, the conceptual and computational complexity of the continuous-time FTF is reduced in comparison to the to that of the discrete-time FTF. The rate of parameter updating in the continuous-time FTF configuration is essentially independent of the bandwidth and center frequency of the processed signal. Consequently, the gain-update module of the proposed algorithm can be implemented with slow devices (or with digital hardware), whereas the signal-path filter must match the frequency characteristics of the processed signal.