Alternative implementations for the frequency-domain LMS adaptive filter

Alternative implementations are presented for the frequency-domain LMS (least-mean-square) adaptive filter first introduced by Narayam and Peterson (1981). The implementation suggested there was a bank of bandpass filters implemented by the discrete Fourier transform (DFT). One of the present implementations is based on the recent paper of B. Widrow et al. (1987) that shows that it is possible to compute the DFT by using the LMS steepest-descent algorithm of Widrow and Hoff. This new implementation is very modular. and requires fewer computations for large filter lengths. This is because the transform part requires O (2N) computations per input sample where N is the filter length while the conventional method of taking FFTs requires O(N log N) computations per input sample. Some results of analysis of convergence are presented. Simulations of practical applications of frequency-domain LMS adaptive filters are carried out to determine its suitability, and comparisons are made with simulations using the FFT. A similar structure cannot be suggested for real data. Instead, a frequency-sampling implementation is proposed, using the recursive computation of the discrete Hartley transform