Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles

Journal of Inequalities and Applications

Mawardi Bahri¹ 

[1] Department of Mathematics, Hasanuddin University, 90245, Makassar, Indonesia;

关键词: Windowed linear canonical transform;    Uncertainty principle;    Orthogonality relation;    42A38;    15A66;    83A05;    35L05;   

DOI  :  10.1186/s13660-021-02737-1

来源: Springer

【 摘 要 】

The windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.

【 授权许可】

CC BY