🤖 AI Summary
To address the challenge of jointly modeling time-structure coupling dynamics in time-varying graph signals—i.e., vertex-located continuous-time series—within non-Euclidean domains, this paper proposes the Joint Vertex-Time Fractional Fourier Transform (JVF-TFT). For the first time, the fractional Fourier transform is extended to the joint vertex-time domain via the tensor product of the graph Fourier transform and the classical fractional Fourier transform, yielding a tunable-order parametric joint spectral representation. This framework enables sparse representation and localized analysis of non-stationary, non-Euclidean signals while achieving joint spectral energy concentration. Experiments on traffic flow and electroencephalography (EEG) data demonstrate that JVF-TFT significantly outperforms conventional decoupled-domain methods in signal reconstruction accuracy, noise robustness, compression ratio, and discriminative performance.