TFAMamba: A Unified Framework of Time–Frequency Analysis and Selective State-Space Modeling for Anomaly Detection

Time-series anomaly detection (TSAD) faces significant challenges when anomalies manifest as subtle frequency shifts or complex spectral patterns that elude conventional time-domain approaches. To address this, we propose TFAMamba, a unified time–frequency modeling framework that organically integrates time–frequency representation with selective state-space modeling. First, we employ the continuous wavelet transform (CWT) to generate multiresolution time–frequency maps, enabling precise capture of transient events and frequency mutations. Subsequently, a periodicity-aware gating module based on the Rényi entropy is designed to quantify the signal periodicity and adaptively trade off between the time-domain and frequency-domain features by responding sensitively to the peaks of energy concentration. Finally, the fused representations are processed by our novel Cross-Mamba decoder, which is specifically designed to overcome the unidirectional dependency constraints of traditional selective state-space models by facilitating parallel modeling and interactive fusion of temporal and spectral dependencies. Experimental results on the UCR timing anomaly detection benchmark dataset show that the proposed method consistently outperforms the existing state-of-the-art methods in all metrics, verifying its notable advantages in subtle anomaly identification.