Multichannel Transform Domain Adaptive Filtering: a Two Stage Approach and Illustration for Acoustic Echo Cancelation

System identification is the underlying mechanism of adaptive filtering algorithms in the context of acoustic echo cancelation systems. Multichannel system identification is subject to specific problems emerging from spatio-temporal couplings in the input signals of the adaptive filter. This paper presents a generic multichannel transformdomain adaptive filtering approach. It is based upon a two-stage decoupling of the spatio-temporal couplings. The temporal decoupling is yielded by a frequency domain transformation and the spatial decoupling by a further unitary transform. The presented approach reveals strong insights into the fundamental problems of multichannel identification.