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Reconstruction of uniformly sampled signals from non-uniform short samples in fractional Fourier domain

机译：从分数傅里叶域中的非均匀短样本重构均匀采样的信号

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摘要

Signal reconstruction from non-uniform samples, especially for non-stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non-stationary signal processing. For non-stationary discrete-time signals, the reconstruction of uniformly sampled signals from non-uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non-uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non-stationary sequences, which is more critical than that of long sequences. In addition, the average signal-to-noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.
机译：从非均匀样本，尤其是对于非平稳信号的信号重构，是数字信号处理领域中的重要问题。作为一种信号处理工具，分数阶傅里叶变换已被证明可有效解决非平稳信号处理中的问题。对于非平稳离散时间信号，本研究首先从分数傅里叶域中的非均匀样本中重建均匀采样的信号。由于在实际应用中仅收集有限的非均匀样本，为了进行更好的重构，在重构中考虑了两种类型的对称扩展，以克服短非平稳序列周期化中存在的不连续性问题，这比长序列。此外，平均信噪比用于评估具有两种类型的对称扩展的重建性能。通过仿真和两个应用程序来验证所提出的重建方法的有效性。

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