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Functional MRI (fMRI) data-processing methods based on changes in the time domain involve, among other things, correlation analysis and use of the general linear model with statistical parametric mapping (SPM). Unlike conventional fMRI data analysis methods, which aim to model the blood-oxygen-level-dependent (BOLD) response of voxels as a function of time, the theory of power spectrum (PS) analysis focuses completely on understanding the dynamic energy change of interacting systems. We propose a new convolution PS (CPS) analysis of fMRI data, based on the theory of matched filtering, to detect brain functional activation for fMRI data. First, convolution signals are computed between the measured fMRI signals and the image signal of prior experimental pattern to suppress noise in the fMRI data. Then, the PS density analysis of the convolution signal is specified as the quantitative analysis energy index of BOLD signal change. The data from simulation studies and in vivo fMRI studies, including block-design experiments, reveal that the CPS method enables a more effective detection of some aspects of brain functional activation, as compared with the canonical PS SPM and the support vector machine methods. Our results demonstrate that the CPS method is useful as a complementary analysis in revealing brain functional information regarding the complex nature of fMRI time series.