Analytic signals and harmonic measures
Analytic signals and harmonic measures
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DOI：
10.1016/j.jmaa.2005.04.003
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发表时间：
2006-02
影响因子：
1.3
通讯作者：
Tao Qian
中科院分区：
文献类型：
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作者：
Tao Qian
本文证明了HeiΘ（s）=−ieiΘ（s）的一个充要条件，其中H是Hilbert变换，Θ是连续的严格增函数，|Θ（R）|=2π，是dΘ（s）是直线上的调和测度。对于周期情形也建立了相应的结果。本文的研究是基于时频分析理论，对时频分析，特别是分析信号瞬时幅值和瞬时频率的研究具有重要意义。作为副产品，我们介绍了保哈代空间的加权三角级数理论和在各自背景下由调和测度引起的傅里叶变换。
We prove that a sufficient and necessary condition for HeiΘ(s)=−ieiΘ(s), where H is Hilbert transformation, Θ is a continuous and strictly increasing function with |Θ(R)|=2π, is that dΘ(s) is a harmonic measure on the line. The counterpart result for the periodic case is also established. The study is motivated by, and has significant impact to time–frequency analysis, especially to aspects of analytic signals inducing instantaneous amplitude and frequency. As a by-product we introduce the theory of Hardy-space-preserving weighted trigonometric series and Fourier transformations induced by harmonic measures in the respective contexts.