Delay lines using self-adapting time constants
Transversal filters using ideal tap delay lines are a popular form of short-term memory based filtering in adaptive systems. Some applications where these filters have attained considerable success include system identification, linear prediction, channel equalization and echo cancellation. The gamma filter improves on the simple FIR delay line by allowing the system to choose a single optimal time-constant by minimizing the Mean Squared Error ofthe system. However, in practice it is difficult to determine the optimal value of the time constant since the performance surface is nonconvex. Also, many times a single time constant is not sufficient to well represent the input signal. We propose a nonlinear delay line where each stage of the delay line adapts its time constant so that the average power at the output of the stage is a constant fraction of the power at the input to the stage. Since this adaptation is independent of the Mean Square Error, there are no problems with local minima in the search space. Furthermore, since each stage adapts its own time constant, the delay line is able to represent signals that contain a wide variety of time scales. We discuss both discrete- and continuous-time realizations of this method. Finally, we are developing analog VLSI hardware to implement these nonlinear delay lines. Such an implementation will provide fast, inexpensive, and low-power solutions for many adaptive signal processing applications.