Open Journal of Statistics

Volume 5, Issue 7 (December 2015)

ISSN Print: 2161-718X   ISSN Online: 2161-7198

Google-based Impact Factor: 0.82  Citations  h5-index & Ranking

On Inversion of Continuous Wavelet Transform

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DOI: 10.4236/ojs.2015.57071    3,563 Downloads   4,670 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.

Share and Cite:

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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