Multi-channel sampling theorems for band-limited signals with fractional Fourier transform |
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Authors: | Feng Zhang Ran Tao and Yue Wang |
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Affiliation: | (1) Department of Electronic Engineering, Beijing Institute of Technology, Beijing, 100081, China |
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Abstract: | Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and
multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal
processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform.
In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the
generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled
signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly
sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting
and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters,
we can obtain reconstruction methods for other sampling strategies.
Supported partially by the National Natural Science Foundation of China (Grant Nos. 60232010 and 60572094) and the National
Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104) |
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Keywords: | fractional Fourier transform fractional band-limited signals fractional filter interpolation series periodic nonuniformly sampled signal |
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