Generalized Fractional Stockwell and Wavelet Transforms

Since the introduction of the fractional Fourier transform by V. Namias in 1980, the subject of fractional integral transformations has flourished and expanded in different directions. The Stockwell transform, which is widely used in frequency analysis, turns out to be related to the continuous wavelet transform. Several fractional Stockwell and wavelet transforms have been introduced in the scientific literature in the last decade. In this talk we discuss the relationship between the Stockwell and the continuous wavelet transforms and then present generalizations of these transforms using a novel convolution operation. Properties of these transforms are presented.