Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.

中文翻译：

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图信号的最优分数阶傅立叶滤波


图信号处理最近受到了相当多的关注。信号处理中的一些概念、工具和应用（例如滤波、变换和采样）已扩展到图形信号处理。此类扩展之一是最优过滤问题。原始图信号的最小均方误差估计可以从其失真和噪声版本中获得。然而，信号和噪声的最佳分离以及最小误差并不总是在普通傅里叶域中实现，而是在分数傅里叶域中实现。在这项工作中，图信号的最优滤波问题被扩展到分数傅里叶域，并提供了所提出问题的理论分析和解决方案以及计算成本的考虑。给出的数值结果说明了分数傅里叶域中滤波的好处。