A gradient algorithm for adaptive orthogonal FIR filter banks with arbitrary magnitude constraints

In this paper, we present a novel gradient-based algorithm for adapting a multichannel FIR filter bank under channel orthogonality and magnitude response constraints. The technique is the multichannel extension of a previously-derived approach for single-channel phase-only adaptive filtering. The algorithm is simple, requiring about four multiply/adds per adaptive filter coefficient to implement. We prove that the differential form of the algorithm maintains the magnitude and orthogonality constraints implicitly through its adaptation. Computer simulation results are provided which confirm the accurate performance of the algorithm in modeling paraunitary systems.