Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper,with a filterbank interpretation of sampling schemes,the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are presented. Firstly,the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then,the particularly efficient filterbank implementations for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last,the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated,which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies.
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
