Analog hardware implementation of continuous-time adaptive filter structures

We have implemented a four-tap adaptive filter in a continuous-time analog VLSI circuit. Since an ideal delay is impossible to implement in continuous -time hardware, we implemented the delay line as a cascade of lowpass filte rs (called the gamma filter). Since many years of research in our lab has s hown that the gamma filter outperforms the ideal delay line for a wide rang e of applications, the gamma filter should not be considered merely a crude approximation of the ideal delay line. We show measured results from an an alog chip that solves the problem of system identification-identifying an u nknown linear circuit from its input/output relationship. Furthermore, we b elieve that a cascade of all-pass filters (called the Laguerre filter) will potentially outperform the gamma. We have built an adaptive Laguerre filte r and show that its measured convergence rate is superior to that of the ga mma. Finally, rather than perform gradient descent on a multimodal error fu nction to determine a single optimal time constant, we propose multi-scale realizations of these delay line structures.