A systematic technique for optimizing multiple branch FIR filters for sampling rate conversion

A systematic approach is proposed for designing a class of special linear-phase FIR filters, called multiple branch filters, for sampling rate conversion such that the multiplication rate is minimized. The proposed filters consist of two basic parts. First, as for the polyphase decomposition, the first filter part is implemented using several branches. For the polyphase decomposition, the overall transfer function is constructed using D branches, where D is the sampling rate conversion ratio, and each branch is expressible as z^-(k-1)B_k(z^D) for k=1, 2, ···, D. The key idea in reducing the arithmetic complexity in implementing the first filter part is based on the following two facts. First, the first part is expressed as A_k(z)B_k(z^D) for k=1, 2, ···, K, where K is only two or three. Second, both the A_k(z)´s are, instead of delay terms z^-(k-1), and the B(z^D)´s are, instead of nonlinear-phase FIR filters, linear-phase FIR filters with either symmetrical or anti-symmetrical impulse responses, enabling one to exploit the coefficient symmetries in the implementation.