A Kind Of Operator Reconstruction Of Fractional Fourier Transform

The Fractional Fourier Transform is the extension of the classical Fourier Transform, when fractional order increases gradually from 0 to 1, the Fractional Fourier Transform of signal can offer much more time-frequency united representation of signal than the classical Fourier Transform, Fractional Fourier Transform can provide extensive optional space for possible signal processing.The multiplicity of FRFT is generated by the disunity of arbitrary power of the complex eigenvalue (μn = {1 , j , ?1 ,? j}) and the different choice of eigenvectors.The main work of this paper is to study the relationship between the Multi-plicity of FRFT in term of the sampling, but, not previous equal interval sampling in all period , we mainly study equal interval sampling at any , , and analyze the sampling theorem in domain of the fraction and the reconstruction formula. Finally we get reconstruction formula. Furthermore, we study the coefficients of the reconstruction formula and find some relationship between the coefficients of reconstruction formula and some classical feature. [0, T p][0, T1 ]0 < T1≤Tp...