| The Fractional Fourier Transform (FRFT) is an extension of the classical Fourier transform. When fractional order increases gradually from 0 to 1, the fractional Fourier transform of signals can offer much more time-frequency united representation of signal than the classical Fourier transform, and can provide extensive optional space for possible disposal of signal. The multiplicity of FRFT is generated by the disunity of the eigenvalue's arbitrary power and the different choice of eigenvectors. These two things are what we will study in sectionâ…¢. We call them GS (generating sequence) and PS (perturbing sequence). In this section we will study the impact of the two and the relationship between them. Of course, there are some other ways to observe the problem. One of them is to consider the period and the distribution of eigenspace. These are what we will study in sectionâ…¡. In this section we will give two operators with period 3 and study their properties. For the importance of FT in signal processing, the most important step from theory to practice is to change the digital signal into analog signal by the method of sampling. So, if the sampling of the operator has been studied enough it will be very useful to the study of the FRFT of signals and their reconstruction. The main work of this paper is to study the sampling theorem in domain of the fraction and the sampling relationship. We will try to obtain the theoretic sampling rate and the proof of feasibility. And we also give some relationship between the kernels under the meaning of sampling.
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