Frequency-Domain Adaptive Filters

5.7 Summary

In many applications when an adaptive filter is required, frequency-domain algorithms (when well optimized) can be extremely good alternatives to time-domain algorithms or adaptive algorithms in subbands. First, the complexity can be made low by utilizing the computational efficiency of the FFT. The delay can be kept as small as desired since the block size is independent of the length of the adaptive filter. Finally, the convergence rate can be relatively good if some parameters of these algorithms such as the exponential window, regularization factor, and adaptation step size are properly chosen. The objective of this chapter was to present a general framework for frequency-domain adaptive filtering. We have shown that an exact algorithm can be derived from the normal equations after minimizing a block least-squares criterion in the frequency domain. We have shown the convergence conditions for this algorithm and have introduced various approximations that lead to well-known algorithms such as the FLMS, UFLMS, and MDF. Other approximations are possible that may lead to some interesting algorithms. We have also shown that APA and MDF are strongly related. Finally, we have generalized some of these ideas to the multichannel case.