In this supplemental material, we provide supplemental information (PDF document with derivations of the results presented in the paper and two additional use cases) and the supplementary video for uncertainty-aware spectral analysis. We model an uncertain time series as a multivariate Gaussian process. We propagate the uncertainty and explicitly compute the probability distribution in the spectral domain. In the video, we use our interactive visual analysis tool to analyze these distributions. This material complements the paper on Uncertainty-aware Spectral Visualization.