Analysis of the transient behavior of unconstrained frequency-domain adaptive filters

Frequency-domain adaptive filters have gained increased attraction, especially for acoustic applications such as echo canceling, active noise control etc. Nevertheless, a theoretical analysis of their transient behavior, which could considerably simplify the design of such filters, is not yet available. For filters which are based on the so-called “overlap-save” technique, we derive analytic expressions describing the transient behavior of the averaged parameter vector and the MSE (mean squared error). Similar to the “independence” theory allowing the time-domain LMS (least mean square) algorithm to be analyzed, we propose some well-defined approximations making the analysis tractable. We show that the obtained simple analytic expressions thereof coincide for any reasonable step-size factors with the corresponding simulations