%0 Journal Article %T On Inversion of Continuous Wavelet Transform %A Lintao Liu %A Xiaoqing Su %A Guocheng Wang %J Open Journal of Statistics %P 714-720 %@ 2161-7198 %D 2015 %I Scientific Research Publishing %R 10.4236/ojs.2015.57071 %X

This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, waveletĄ¯s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that waveletĄ¯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.

%K Continuous Wavelet Transform %K WaveletĄ¯s Dual %K Inversion %K Normal Wavelet Transform %K Time-Frequency Filtering %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=62028