Graph Fractional Hilbert Transform, Analytic Signal, and Its Application to ECG Classification

This paper presents a unified framework for graph fractional analytic theory, extending classical analytic signal concepts to the graph fractional domain. Specifically, we introduce the graph fractional Hilbert transform, the graph fractional analytic signal framework based on the conjugate symmetry property of the graph fractional Fourier transform, and graph fractional amplitude modulation (AM) and frequency modulation (FM) concepts. We analyze fundamental properties including linearity, orthogonality preservation, and shift-invariance. The proposed framework is applied to electrocardiogram (ECG) signal classification, where graph fractional AM and FM features capture critical waveform characteristics, leading to improved classification performance compared to traditional methods.