Coupled 2<i>D</i>-Fractional Wavelet Transform

Abstract

We introduce a new fractional wavelet transform using the convolution for the coupled fractional Fourier transform. We derive that the fractional wavelet transform satisfies all the expected properties such as Parseval identity, inversion formula, convolution theorem. We also characterize the range of the fractional wavelet transform on . Finally, we establish the uncertainty principle for the fractional wavelet transform.