On the closeness of the space spanned by the lattice structures for a class of linear phase perfect reconstruction filter banks
On the closeness of the space spanned by the lattice structures for a class of linear phase perfect reconstruction filter banks
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DOI：
10.1016/j.sigpro.2009.06.021
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Zhiming Xu;A. Makur
中科院分区：
文献类型：
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作者：
Zhiming Xu;A. Makur
对于滤波器长度L>2M的M通道FIR线性相位完全重构滤波器组（LPPRFBs），已有文献证明了现有格结构的不完备性，甚至最近也有报道称不存在完整的一阶格结构。因此，自然会出现一个问题，即现有晶格结构所跨越的空间有多大，以及它在某些多项式变换下的接近程度。对这一问题的研究可以揭示基于格点的LPPRFB设计具有何种意义上的最优性。受此启发，本文首先研究了任意等长LPPRFB在多项式变换下，现有格结构所张成的空间的封闭性。我们已经表明，这个空间是封闭的流行的多项式变换下广泛使用的FB设计，这建立了次优的LPPRFBs基于格的设计方法。此外，在变换前后的晶格参数之间的显式关系已被示出，用于描述由这些晶格结构所跨越的空间的接近程度。
The incompleteness of the existing lattice structures has been well established for M-channel FIR linear phase perfect reconstruction filter banks (LPPRFBs) with filter length L>2M in the literature, and even the nonexistence of complete order-one lattice has been reported recently. Thus, a question arises naturally as to how large the space spanned by the existing lattice structure is, and about its closeness over some polynomial transformations. The study for such issue can reveal what sense of optimality the lattice based design for LPPRFBs possesses. Inspired from this perspective, this paper firstly studies the closeness of the space spanned by the existing lattice structures under the polynomial transformations for arbitrary equal-length LPPRFBs. We have shown that this space is closed under the popular polynomial transforms widely used in FB design, which establishes the suboptimality of the lattice based design methods for LPPRFBs. Furthermore, the explicit relationship between the lattice parameters before and after transformations has been shown for describing the closeness of the space spanned by those lattice structures.