Novel Fractional Wavelet Transform with Closed-Form Expression

A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages...

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Bibliographic Details
Published inInternational journal of advanced computer science & applications Vol. 5; no. 1
Main Authors O., K., A., R., M., S., Ochonogor, O.
Format Journal Article
LanguageEnglish
Published West Yorkshire Science and Information (SAI) Organization Limited 2014
Subjects
Fourier transforms
Rotation
Wavelet transforms
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Summary:A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown.
ISSN:2158-107X
2156-5570
DOI:10.14569/IJACSA.2014.050126