Equal convergence conditions for normal- and partitioned-frequency domain adaptive filters

Convergence characteristics of adaptive filters are influenced by statistical properties of the input signal. In order to remove this dependency, decorrelation can be applied with a frequency- domain adaptive filter (FDAF), in which the length M of the transformation between the time and the frequency domain is chosen to be equal to the length N of the adaptive filter. The relevant length M is determined by the statistical properties of the input signal and needs not to be equal to N. Both lengths M and N can be decoupled by using partitioned frequency-domain adaptive filters (PFDAFs). Statistical conditions are derived for the input signal in such a way that both PFDAF and FDAF have equal convergence properties.