Multidimensional fractional Fourier transform: Properties and applications
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Date
2025
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Faculty of Sciences
Abstract
This master s thesis focuses on the study of the multidimensional fractional Fourier
transform in both its classical and windowed forms as a powerful extension of the con-
ventional Fourier transform with enhanced capability for analyzing non-stationary sig-
nals. The work presents formal de nitions of both transforms and explores their main
mathematical properties, including linearity, time-shift, convolution, scaling, and en-
ergy preservation. Special attention is given to the role of window function in improving
time-frequency localization in the n-dimensional window fractional Fourier transform
framework. A comparative analysis between these transforms is also provided. Finally,
selected applications are presented to highlight the relevance of these transforms in
various elds