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On Inversion of Continuous Wavelet Transform

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DOI: 10.4236/ojs.2015.57071    3,086 Downloads   3,539 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Liu, L. , Su, X. and Wang, G. (2015) On Inversion of Continuous Wavelet Transform. Open Journal of Statistics, 5, 714-720. doi: 10.4236/ojs.2015.57071.

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