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Spectral Analysis of Sampled Band-Limited Signals in the Offset Linear Canonical Transform Domain

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Abstract

The spectral analysis of sampled signals is one of the fundamental topics in the signal processing community. The properties and applications of uniformly and periodic nonuniformly sampled one- or two-dimensional signals in the traditional Fourier domain have been extensively studied. As the offset linear canonical transform (OLCT) has been shown to be a powerful tool for signal processing and optics, it is therefore worthwhile and interesting to consider the spectral analysis of sampled signals in the OLCT domain. In this paper, we investigate the spectrum of uniformly and periodic nonuniformly sampled one- and two-dimensional signals in the OLCT domain. First, the general spectral representation of uniformly sampled one-dimensional signals has been obtained. The reconstruction formula for uniform sampling from one-dimensional signal also has been performed. Based on the results, these theories are all extended to the two-dimensional case. Second, the digital spectra of periodic nonuniformly sampled one- and two-dimensional signals have been derived analytically. Finally, exhaustive analysis of sampled chirp signals in the OLCT domain has been carried out, and the simulations are presented to verify the correctness of the the results.

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Acknowledgments

The authors would like to thank the editor and the anonymous referees for their valuable comments and suggestions that improved the clarity and quality of this manuscript. This work was supported by the National Natural Science Foundation of China (61374135) and China Central Universities Foundation (CDJZR11170010).

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Correspondence to Shuiqing Xu.

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Xu, S., Chai, Y. & Hu, Y. Spectral Analysis of Sampled Band-Limited Signals in the Offset Linear Canonical Transform Domain. Circuits Syst Signal Process 34, 3979–3997 (2015). https://doi.org/10.1007/s00034-015-0053-1

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