The use of analog adaptive filters in modern integrated systems is limited by the complexity of the analog adaptation hardware and by dc offset effects which limit the adaptation accuracy. Both problems can be addressed by using an analog filter with a digital adaptation algorithm.

The design of digitally programmable analog filters suitable for adaptive applications is examined. Novel Gm-C circuits are described and implemented in a CMOS prototype 5th order integrated filter with digitally programmable poles and zeros. However, the greatest challenge associated with performing digital adaptation of an analog filter is obtaining the gradient information without overcomplicating the analog design. Three main approaches to overcoming this challenge are described. First, the gradient information is obtained by correlating changes in the output squared error to independent dither on the adapted parameters. Second, the internal state signals (and, hence, the gradient signals) are calculated from a time delayed input vector using a co-ordinate transformation. Third, time delayed estimates of the filter input are obtained digitally from the filter output and used to calculate the required gradient signals. All three techniques use digital signal processing to obtain the gradient information and require little, if any, additional analog hardware. The performance of the new adaptive algorithms are discussed and several variations are proposed to simplify integrated implementations. The prototype integrated analog filter was used as a testbed to verify two of the novel algorithms. Gradient descent optimization of analog filter parameters was successfully performed without access to any of the filter's internal state signals, which was not previously possible. As a result, designers of analog adaptive filters are now free to perform the filter design without being restricted by the requirements of the adaptation algorithm.