The authors propose a fast adaptive least-squares algorithm for linear-phase finite-impulse-response (FIR) filters. The algorithm requires 10m multiplications per data point where m is the filter order. This reduced computation stems from the fast adaptive forward-backward least-squares method. Both linear-phase cases i.e. with constant phase delay and with constant group delay, are examined. Simulation results demonstrate that the proposed algorithm is superior to the least-mean-squares gradient algorithm and the averaging scheme used for the modified fast Kalman algorithm.>

Performance and realization of finite impulse response (FIR) digital filters that use an adaptive delta modulator as an analog/ digital converter have been studied. These filters require no multiplication and offer many advantages over conventional PCM filters including low power consumption, small size, and cost effectiveness. Analytical formulas have been derived for the expected mean-squared errors and also for the word length necessary to achieve the desired performance. Computer simulation has been done to optimize the parameter values and to verify the results of performance analysis. In addition, design of FIR ADM digital filters for processing single and multichannel signals has been considered.