Mixed-Radix Fast Filter Bank Approach for the Design of Variable Digital Filters With Simultaneously Tunable Bandedge and Fractional Delay

A popular technique to design variable fractional delay (VFD) filters or variable bandedge filters is the polynomial based finite impulse response (FIR) filters, where each filter coefficient is approximated as a polynomial of the variable parameter. However, if the filter is required to have both VFD and variable bandedge, the computational complexity becomes very high, because two-dimensional polynomials have to be used, provided that the same polynomial idea is followed. In this paper, a filter bank approach is proposed for the design of VFD filters. The basic idea of the approach is to split the full band signals into subbands and each subband is, respectively, shifted by a phase, which is determined by the required fractional delay. The overall fractional delay is achieved by combining all subbands. Using this technique, the variable bandedge could be incorporated into the VFD filter with trivial extra computations. Design examples show that the proposed technique achieves high performance with low computational complexity.