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Functional magnetic resonance imaging (fMRI) time series is nonlinear and composed of components at multiple temporal scales, which presents significant challenges to its analysis. In the literature, significant effort has been devoted into model-based fMRI signal analysis, while much less attention has been directed to data-driven fMRI signal analysis. In this paper, we present a novel data-driven multiscale signal decomposition framework named empirical mean curve decomposition (EMCD). Targeted on functional brain mapping, the EMCD optimizes mean envelopes from fMRI signals and iteratively extracts coarser-to-finer scale signal components. The EMCD framework was applied to infer meaningful low-frequency information from blood oxygenation level-dependent signals from resting-state fMRI, task-based fMRI, and natural stimulus fMRI, and promising results are obtained.