"Affine Wigner distribution"Berge, Stine MarieWe examine the affine Wigner distribution from a quantization perspective and develop a connections to the scalogram through the convolution on the affine group. Building the theory from this perspective, we emphasize the group theoretic properties of the affine Wigner distribution and demonstrate how this illuminates the theory. As a consequence, we show that although the affine Wigner distribution is never analytic, it can be poly-analytic of any order. We strive to unite the literature on affine Wigner distributions and provide the connection to the Mellin transform in a rigorous manner. An affine Wigner approximation problem is considered motivated by recent interest in the analogous problem for the (time-frequency) Wigner distribution. Finally, we discuss some open problems of both theoretical and applied nature. |
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