Abstract: Brain signatures of functional activity have shown promising results in both decoding brain states, meaning distinguishing between different tasks, and fingerprinting, that is identifying individuals within a large group. Importantly, these brain signatures do not account for the underlying brain anatomy on which brain function takes place. Structure-function coupling based on graph signal processing (GSP) has recently revealed a meaningful spatial gradient from unimodal to transmodal regions, on average in healthy subjects during resting-state. Here, we explore the specificity of structure-function coupling to distinct brain states (tasks) and to individual subjects. We used multimodal magnetic resonance imaging of 100 unrelated healthy subjects from the Human Connectome Project both during rest and seven different tasks and adopted a support vector machine classification approach for both decoding and fingerprinting, with various cross-validation settings. We found that structure-function coupling measures allow accurate classifications for both task decoding and fingerprinting. In particular, key information for fingerprinting is found in the more liberal portion of functional signals, with contributions strikingly localized to the fronto-parietal network. Moreover, the liberal portion of functional signals showed a strong correlation with cognitive traits, assessed with partial least square analysis, corroborating its relevance for fingerprinting. By introducing a new perspective on GSP-based signal filtering and FC decomposition, these results show that brain structure-function coupling provides a new class of signatures of cognition and individual brain organization at rest and during tasks. Further, they provide insights on clarifying the role of low and high spatial frequencies of the structural connectome, leading to new understanding of where key structure-function information for characterizing individuals can be found across the structural connectome graph spectrum.