Published Book Chapter Detail

The Generalizations of the Multidimensional Fourier Transform

Karima Kimouche^1*, Abdelouahab Bibi^2*

¹Department of Mathematics, 20 aout 1955 University, Skikda, Algeria

²Department of Mathematics, Mentouri University, Constantine, Algeria

*For Correspondence

k.kimouche@gmail.com

Abd.bibi@mail.com

This work, deal a brief introduction of multidimensional (M—) Fourier transform and its generalization. So, we give the definition of such transformation and we establish their properties enriched by several illustrative examples. Additionally, we give the intrinsic properties of the generalized version as: M—windowed, M—fractional, M—linear canonical transform, and M—quadratic-phase Fourier transforms.

Keywords

Multidimensional Fourier transforms, Windowed Fourier transform, Fractional Fourier transform, Linear canonical transform, Quadratic-phase Fourier transform