The field of sensor-based human activity recognition (HAR) mainly uses posture, motion and context data of Inertial Measurement Units (IMUs) to identify daily activities. Despite the advancements in learning-based methods, it is challenging to perform information fusion from the temporal perspective due to the complexities in fusing heterogeneous sensor data and establishing long-term context correlations. This paper proposes a novel triple spectral fusion framework tailored for HAR. First, we develop an adaptive complementary filtering technique for noise suppression and organize each IMU's sensors into posture and motion modality nodes. Given that IMU nodes form a dynamic heterogeneous graph, we then apply adaptive filtering within the graph Fourier domain to merge both homogeneous and heterogeneous node information. Furthermore, an adaptive wavelet frequency selection approach is implemented to suppress context redundancy and shorten the length of features. This approach enhances both timestamp-based graph aggregation and the correlation of long-term contexts. Our framework uses adaptive filtering in the Fourier, graph Fourier, and wavelet domains, enabling effective multi-sensor fusion and context correlation. Extensive experiments on ten benchmark datasets demonstrate the superior performance of our framework. Project page: https://github.com/crocodilegogogo/TSF-TPAMI2026.

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