Abstract
The aim of this study is to construct both the continuous and discrete special affine wavelets in . Firstly, we introduce the continuous special affine wavelet transform via the convolution operations in the special affine Fourier domain. Subsequently, we investigate all the fundamental properties of the proposed transform using special affine Fourier transforms. Secondly, the discrete orthonormal special affine wavelets are constructed by introducing the notion of the special affine multiresolution analysis (MRA) in . Besides, a fast wavelet transform associated with special affine MRA is also presented. Towards the culmination, the formulation of special affine MRA starting from a given scaling function is briefly studied.
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