文章基本信息

标题：On Inversion of Continuous Wavelet Transform
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作者：Lintao Liu ; Xiaoqing Su ; Guocheng Wang 等
期刊名称：Open Journal of Statistics
印刷版ISSN：2161-718X
电子版ISSN：2161-7198
出版年度：2015
卷号：05
期号：07
页码：714-720
DOI：10.4236/ojs.2015.57071
语种：English
出版社：Scientific Research Publishing
摘要：This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.
关键词：Continuous Wavelet Transform;Wavelet’s Dual;Inversion;Normal Wavelet Transform;Time-Frequency Filtering