Graph spectral representations are fundamental in graph signal processing, providing a rigorous frameworkforanalyzing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the graph Fourier transform (GFT) through a fractional-order parameter, enabling flexible spectral analysis with mathematical consistency. The angular graph Fourier transform (AGFT) further introduces angular control by rotating GFT eigenvectors; however, existing constructions may fail to reduce exactly to the GFT at zero angle, weakening theoretical consistency and interpretability. To address these complementary limitations, namely the lack of rotation-based basis control in GFRFT and the defective zero-angle degeneracy of AGFT, this paper proposes the rotation-parameterized graph fractional Fourier transform (RP-GFRFT), which unifies fractional order and rotation-parameterized spectral analysis. A degeneracy preserving rotation matrix family is constructed to guarantee exact GFT reduction at zero angle. TwoRP-GFRFTvariants,I-RP-GFRFTandII-RP-GFRFT,arethenformulated, with theoretical analyses confirming their unitarity, invertibility, reduction behavior, and smooth parameter dependence. The fractional order and rotation angle are jointly optimized for adaptive graph spectral filtering. Experiments on real-world signals, images, and point clouds demonstrate that RP-GFRFT improves denoising accuracy, reconstruction quality, and feature preservation over GFRFT, AGFT, and representative filtering baselines.

翻译：图谱表示是图信号处理的基础，为分析图结构数据提供了严谨框架。图分数傅里叶变换通过引入分数阶参数扩展了经典图傅里叶变换，在保持数学一致性的同时实现了灵活的谱分析。角度图傅里叶变换进一步通过旋转图傅里叶变换特征向量引入角度控制；然而，现有构造方法在零角度时可能无法精确退化为图傅里叶变换，削弱了理论一致性与可解释性。为解决这些互补性局限（即图分数傅里叶变换缺乏基于旋转的基控制及角度图傅里叶变换存在零角度退化缺陷），本文提出旋转参数化图分数傅里叶变换，统一了分数阶与旋转参数化的谱分析。通过构造退化保持旋转矩阵族，确保在零角度时精确退化为图傅里叶变换。继而提出两种变体（I型旋转参数化图分数傅里叶变换与II型旋转参数化图分数傅里叶变换），理论分析证实其具有酉性、可逆性、退化行为及平滑参数依赖性。通过联合优化分数阶与旋转角实现自适应图谱滤波。在真实信号、图像与点云上的实验表明，旋转参数化图分数傅里叶变换相较于图分数傅里叶变换、角度图傅里叶变换及代表性滤波基线方法，在去噪精度、重建质量与特征保留方面均有提升。