Quantization of TF lattice-invariant operators on elementary LCA groups
Quantization of TF lattice-invariant operators on elementary LCA groups
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DOI：
10.1007/978-1-4612-2016-9_8
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
H. Feichtinger;W. Kozek
中科院分区：
文献类型：
--
作者：
H. Feichtinger;W. Kozek
初等局部紧阿贝尔群9是时频分析的抽象观点的自然设置。函数空间Gelfand三元组（So，L ~ 2，S~）（Q）适用于抽象TF-平面9 × 9上的采样和周期化过程，它允许定义线性算子的”调和分析与综合”的广义Kohn-Nirenberg对应.我们将Gabor原子的对偶性和双正交性的概念推广到任意9 × 9的具有紧商的离散子群。基本莱亚组的设置不仅是一个标准的Gabor分析的扩展，但承认一个统一的制定连续时间，离散时间，周期性和多维信号，包括不可分的晶格和/或不可分的原子的情况下。
Elementary locally compact abelian groups 9 are a natural setup for an abstract view on time-frequency (TF) analysis. The function space Gelfand triple (So, L2, S~)(Q) is adapted to the sampling and periodization procedures on the abstract TF-plane 9 x 9 and it allows the definition of a generalized Kohn-Nirenberg correspondence for a" harmonic analysis and synthesis" of linear operators. We extend the concept of duality and biorthogonality of Gabor atoms to arbitrary discrete subgroups of 9 x 9 with compact quotient. The setting of elementary LeA groups is not only an extension of standard Gabor analysis but admits a unified formulation for continuous-time, discrete-time, periodic, and multidimensional signals including the case of nonseparable lattices and/or nonseparable atoms.