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On Inversion of Continuous Wavelet Transform

DOI: 10.4236/ojs.2015.57071, PP. 714-720

Keywords: Continuous Wavelet Transform, Wavelet’s Dual, Inversion, Normal Wavelet Transform, Time-Frequency Filtering

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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.

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