Generalized adaptive IFIR filter bank structures

Adaptive filters based on filter bank (FB) techniques have attracted attention recently due to their ability to improve convergence rate and reduce the computational complexity. This paper investigates a generalized adaptive interpolated finite impulse response (IFIR) FB structure. The IFIR model is a set of cascade of an interpolator and a sparse filter connected in parallel. The IFIR FB models the system impulse response as a linear combination of double indexed set of functions. The modeling capabilities and delay properties of the structure are investigated. Realizations of adaptive IFIR FB structures with delaying and delayless properties are presented. The delaying structure is obtained by employing orthogonal set of the basis functions for the interpolating FB. It is shown that delayless adaptive IFIR FB structure, as a special case of general adaptive IFIR FB, can be obtained by relaxing the orthogonality condition on the basis functions. This allows flexibility to choose the interpolators. The interpolators could be chosen to improve convergence rate of the adaptive algorithm. In general, optimal design of interpolator FB requires a priori knowledge of the input process and the system. One method of choosing the interpolators is by a non-linear optimization procedure based only on a priori knowledge of input process. We present a new method to adapt the interpolators themselves based on a common cost function and hence require no a priori knowledge of the input statistics. The convergence rate and steady state error performance of these structures are compared with the classical fullband filter in system identification scenario. Its application in acoustic echo cancellation (AEC) is presented.