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高妮, 蒋英春. 特殊仿射傅里叶变换域上带限随机信号的重构误差估计J. 桂林电子科技大学学报, 2025, 45(2): 203-207. DOI: 10.16725/j.1673-808X.2022308
引用本文: 高妮, 蒋英春. 特殊仿射傅里叶变换域上带限随机信号的重构误差估计J. 桂林电子科技大学学报, 2025, 45(2): 203-207. DOI: 10.16725/j.1673-808X.2022308
GAO Ni, JIANG Yingchun. Reconstruction error estimation of bandlimited random signals in the special affine Fourier transform domainJ. Journal of Guilin University of Electronic Technology, 2025, 45(2): 203-207. DOI: 10.16725/j.1673-808X.2022308
Citation: GAO Ni, JIANG Yingchun. Reconstruction error estimation of bandlimited random signals in the special affine Fourier transform domainJ. Journal of Guilin University of Electronic Technology, 2025, 45(2): 203-207. DOI: 10.16725/j.1673-808X.2022308

特殊仿射傅里叶变换域上带限随机信号的重构误差估计

Reconstruction error estimation of bandlimited random signals in the special affine Fourier transform domain

  • 摘要: 特殊仿射傅里叶变换具有额外的自由度,变换更加灵活,已被证明是信号处理、光学以及通信等领域的一种强有力的分析工具。对于重构误差的估计问题,特殊仿射傅里叶变换域上带限随机信号的均匀采样定理虽然已经建立,但是至今未见关于重构误差的估计。由于重构中存在各种各样的误差,可能会影响重构的精度,且所有的重构公式都是理想的,因此,误差估计的研究在采样定理中的应用十分重要,基于此,研究特殊仿射傅里叶变换域上带限随机信号均匀采样与重构中的2种误差估计,即混淆误差估计和截断误差估计。首先,简要介绍了特殊仿射傅里叶变换的基本知识和均匀采样模型。然后,推导了2种误差估计。

     

    Abstract: Special affine Fourier transforms have additional degrees of freedom and are more flexible, and have proven to be a powerful analytical tool in the fields of signal processing, optics, and communications. For the estimation of reconstruction errors, although the uniform sampling theorem for band-limited random signals in the special affine Fourier transform domain has been established, no estimation of reconstruction errors has been found so far. Because there are various errors in the reconstruction, which may affect the accuracy of the reconstruction, and all the reconstruction formulas are ideal, it is very important to study the application of error estimation in the sampling theorem , Based on this, this paper mainly studies two kinds of error estimators in uniform sampling and reconstruction of bandlimited random signals in special affine Fourier transform domain, namely, aliasing error estimator and truncation error estimator. Firstly, the basic knowledge of special affine Fourier transform and uniform sampling model are briefly introduced. Then, two kinds of error estimates are derived.

     

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