Hybrid Structures for Low-Complexity Variable Fractional-Delay FIR Filters

This paper proposes a pair of new structures for implementing low-complexity odd-order and even-order variable fractional-delay (VFD) FIR filters using hybrid structures with both even-order and odd-order subfilters. For odd-order VFD filter design, the main idea is to replace the conventional even-symmetric odd-order (type-2) subfilters with the cascade of a type-2 half-delay filter and even-symmetric even-order (type-1) subfilters. This is because the magnitude responses of type-2 subfilters are zero at frequency ?? = ??, which causes large approximation errors, especially for wideband VFD filter design. Similarly, for even-order VFD filter design, the conventional odd-symmetric even-order (type-3) subfilters are replaced with the cascade of a type-2 half-advance filter and odd-symmetric odd-order (type-4) subfilters. This replacement avoids the zero magnitude responses at frequency ?? = ?? of type-3 subfilters and makes low-complexity wideband VFD filter design possible. As compared with the existing Farrow structures with either odd-order subfilters (odd-order design) or even-order subfilters (even-order design), the hybrid structures consist of three types of FIR filters (type-1 and type-4 subfilters, as well as type-2 half-delay or half-advance filter). Replacing type-2 subfilters with type-1 ones (odd-order design) and replacing type-3 subfilters with type-4 ones (even-order design) can significantly reduce the VFD filter complexity for wideband designs. Design examples are given to illustrate the effectiveness of both odd-order and even-order hybrid structures.