Odd-order Variable Fractional-delay Filters Research Articles

Multisegment optimization design of variable fractional-delay FIR filters

This paper presents a multisegment optimization design algorithm for both even- and odd-order variable fractional-delay filters. The proposed algorithm is based on segmenting the fractional delay and separately solving the filter coefficients in each segment. Moreover, the lower bound of the polynomial order and the upper bound of the subfilter design error are derived. These bounds enable us to prove that the proposed algorithm effectively reduces the implementation complexity at the expense of storage resources. Hence, a joint search algorithm is proposed to find the lowest polynomial orders and subfilter orders that meet the filter specifications. Simulations and comparisons are conducted to illustrate the superiority of the proposed algorithm in terms of the implementation complexity over existing methods under common specifications.

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.

Symmetric Structures for Odd-Order Maximally Flat and Weighted-Least-Squares Variable Fractional-Delay Filters

Our previous work has shown that coefficient symmetry can be exploited for designing high-accuracy and low-complexity even-order variable fractional-delay (VFD) filters. The objectives of this paper are twofold; One is to derive a coefficient symmetry for odd-order VFD filters, and then formulate a closed-form weighted-least-squares (WLS) design. Exploiting the coefficient symmetry along with different-order subfilters reduces the number of independent VFD filter coefficients by more than 50% , and thus reduces the hardware cost and the number of multipliers by more than 50%. Another objective is to briefly derive the maximally flat (MF) VFD filters from Nth-degree polynomial interpolation, and then present two kinds of transformation matrices for transforming causal odd-order MF VFD filters into symmetric structures such that the filter complexity can be reduced. As a result, both WLS and MF VFD filters can be implemented as the Farrow structure with significantly reduced complexity, which facilitates high-speed VFD filtering. Various examples are given to illustrate the effectiveness of the symmetry-based design and implementations.