On the comparison of optimum least-squares and computationally efficient DFT-based adaptive block filters

In this paper, we discuss a general frequency-domain adaptive algorithm, which can be implemented very efficiently, the so-called partitioned frequency-domain least-mean-square (PFLMS) algorithm. In comparing this PFLMS algorithm with the optimum block recursive least-squares (BRLS) algorithm, we consider its tracking behaviour, i.e., the ability to track changes of the unknown plant. We discuss the design of the PFLMS algorithm by investigating the selection of its free parameter, the DFT length. We show that for typical applications, such as cancelation of acoustic echos and active noise control, it can be designed such that its tracking behaviour is optimum. We emphasize that such an optimally designed PFLMS algorithm cannot be improved, e.g., by reusing the input data.