Hybrid Structures for Low-Complexity Variable Fractional-Delay FIR Filters
Hybrid Structures for Low-Complexity Variable Fractional-Delay FIR Filters
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DOI：
10.1109/tcsi.2009.2025848
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发表时间：
2010-04
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影响因子：
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通讯作者：
T. Deng
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文献类型：
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作者：
T. Deng
本文提出了一种利用奇数阶子滤波器和偶数阶子滤波器的混合结构实现低复杂度奇数阶和偶数阶变分数延迟(VFD)FIR滤波器的新结构。对于奇数阶VFD滤波器的设计，其主要思想是用二类半延迟滤波器和偶数对称偶数阶(Type-1)子滤波器的级联来代替传统的偶对称奇数阶(Type-2)子滤波器。这是因为二类子滤波器的幅值响应在频率？=？时为零，这会导致很大的逼近误差，特别是对于宽带VFD滤波器的设计。类似地，对于偶数阶VFD滤波器的设计，将传统的奇对称偶数阶(类型3)子滤波器替换为类型2半提前滤波器和奇对称奇数阶(类型4)子滤波器的级联。这种替换避免了三类子滤波器在频率为？=‘时的零幅值响应，并使低复杂度宽带VFD滤波器的设计成为可能。与现有的具有奇数阶子滤波器(奇数阶设计)或偶数阶子滤波器(偶数阶设计)的Farrow结构相比，混合结构由三种类型的FIR滤波器(类型1和类型4子滤波器，以及类型2半延迟或半提前滤波器)组成。将2类子滤波器替换为1类(奇数阶设计)，将3类子滤波器替换为4类(偶数阶设计)，可以显著降低宽带设计中的VFD滤波器的复杂度。给出了设计算例，说明了奇数阶和偶数阶混合结构的有效性。
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.