On shift variance bounds in multi-channel filter banks

Shift variance bounds of critically sampled multirate filter banks are usually defined by using eigensystem analysis of the commutator operator. Computational methods are provided for two-channel FIR filter banks by Aach and Fuhr (2009). This paper investigates shift variance bounds in oversampled multi-channel filter banks and derives some general results which include some of Aach and Fuhr (2009) as special cases. Using polyphase representation, numerical methods are provided to compute the shift variance bounds for arbitrary filter banks. Examples are given to demonstrate the effectiveness of the obtained results.