Parseval Relationship of Samples in the Fractional Fourier Transform Domain

Abstract EN

This paper investigates the Parseval relationship of samples associated withthe fractional Fourier transform.

Firstly, the Parseval relationship for uniformsamples of band-limited signal is obtained.

Then, the relationship isextended to a general set of nonuniform samples of band-limited signal associatedwith the fractional Fourier transform.

Finally, the two dimensionalcase is investigated in detail, it is also shown that the derived results can beregarded as the generalization of the classical ones in the Fourier domain tothe fractional Fourier transform domain.