Mono‐components for decomposition of signals
Mono‐components for decomposition of signals
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DOI：
10.1002/mma.721
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发表时间：
2006-07
影响因子：
2.9
通讯作者：
T. Qian
中科院分区：
文献类型：
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作者：
T. Qian
本文进一步对特征函数问题进行了研究：求f(T)=ρ(T)Eiθ(T)使得Hf=−if，ρ(T)⩾0和θ‘(T)⩾0，A.E.其中H是希尔伯特变换。满足上述条件的函数称为单分量，已在时频分析中寻找到。一些作者对特殊情况ρ≡1进行了系统的研究，并给出了与Möbius变换和Blaschke积有关的演示结果。在这篇注记中，作为一个关键步骤，我们刻画了一般情况下ρ⩾0的特征函数问题的一类基本解。这类解等同于一类特殊的单复变量的星形函数，称为圆形氢原子。它们是圆形单声道组件的积木。我们首先研究单位圆的上下文，然后在直线上推导出相应的结果。文中还研究了双单分量并联的情况。版权所有©2006 John Wiley&Sons，Ltd.
This note further carries on the study of the eigenfunction problem: Find f(t)=ρ(t)eiθ(t) such that Hf=−if, ρ(t)⩾0 and θ′(t)⩾0, a.e. where H is Hilbert transform. Functions satisfying the above conditions are called mono‐components, that have been sought in time‐frequency analysis. A systematic study for the particular case ρ≡1 with demonstrative results in relation to Möbius transform and Blaschke products has been pursued by a number of authors. In this note, as a key step, we characterize a fundamental class of solutions of the eigenfunction problem for the general case ρ⩾0. The class of solutions is identical to a special class of starlike functions of one complex variable, called circular H‐atoms. They are building blocks of circular mono‐components. We first study the unit circle context, and then derive the counterpart results on the line. The parallel case of dual mono‐components is also studied. Copyright © 2006 John Wiley & Sons, Ltd.