In this talk, we will give an overview of statistical methodologies for spectral analysis of time series data. We will briefly discuss the common approaches for spectral analysis, and discuss their limitations for analyzing data whenever the study has a longitudinal experimental design. To address the limitations, we propose a Bayesian model for spectral analysis that accounts for the covariation within a subject. Our proposed model uses smoothing splines to estimate the spectra of the time series, and we induce correlation across visits through the prior distributions of the model parameters. We discuss the merits of our proposed model in the context of a longitudinal fMRI experiment, and we illustrate its utility using simulated and empirical data.