On Inversion of Continuous Wavelet Transform

• 作者: Guocheng Wang Lintao Liu Xiaoqing Su
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Continuous WAVELET TRANSFORM Wavelet’s Dual INVERSION Normal WAVELET TRANSFORM TIME-FREQUENCY FILTERING
• 年，卷（期）: 2015,（7）
• 页码范围: 714-720
• 页数: 7页
• 分类号: O1

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.