Obtaining digital gradient signals for analog adaptive filters

Analog adaptive filters with digitally programmable coefficients can provide speed, power, and area advantages over digital adaptive filters while overcoming the dc offset problems associated with fully analog implementations. However, digital estimates of the filter states and gradient signals must be generated from the filter output in order to perform LMS adaptation. State observers studied in the control literature either require access to the system input or require the system to be minimum phase. Here, approximate time-delayed state estimates are obtained from the filter output by truncating a Taylor series expansion of the inverted nonminimum phase zeros. Simulation results are presented for a 5-tap FIR filter. No steady-state error is introduced by dc and gain offsets.