Parseval relationship of samples in the fractional Fourier transform domain (Q1760687)

Summary: This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signals is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signals 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 a generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.