This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigated in detail, it is also shown that the derived results can be regarded as the generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.
Bing-Zhao Li. Tian-Zhou Xu. "Parseval Relationship of Samples in the Fractional Fourier Transform Domain." J. Appl. Math. 2012 1 - 11, 2012. https://doi.org/10.1155/2012/428142