Designing local orthogonal bases on finite groups I: Abelian case

被引:25
作者
Bernardini, R [1 ]
Kovacevic, J
机构
[1] Univ Padua, I-35131 Padua, Italy
[2] Bell Labs, Murray Hill, NJ 07974 USA
关键词
Abelian Group; Irreducible Representation; Singular Value Decomposition; Finite Group; Filter Bank;
D O I
10.1007/BF02510115
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This, in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considers abelian groups. The second part considers nonabelian groups where, as an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. These bases are useful for building systems for evaluating quality.
引用
收藏
页码:1 / 23
页数:23
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