TITLE:
On Inversion of Continuous Wavelet Transform
AUTHORS:
Lintao Liu, Xiaoqing Su, Guocheng Wang
KEYWORDS:
Continuous Wavelet Transform, Wavelet’s Dual, Inversion, Normal Wavelet Transform, Time-Frequency Filtering
JOURNAL NAME:
Open Journal of Statistics,
Vol.5 No.7,
December
18,
2015
ABSTRACT: 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.