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 low-pass filters (called the gamma filter). Since many years of research in our lab has shown that the gamma filter outperforms the ideal delay line for a wide range of applications, the gamma filter should not be considered merely a crude approximation of the ideal delay line. We show measured results from an analog chip that solves the problem of system identification–identifying an unknown linear circuit from its input/output relationship. Furthermore, we believe that a cascade of all-pass filters (called the Laguerre filter) will potentially outperform the gamma. We have built an adaptive Laguerre filter and show that its measured convergence rate is superior to that of the gamma. Finally, rather than perform gradient descent on a multimodal error function to determine a single optimal time constant, we propose multi-scale realizations of these delay line structures.