Functional near infrared spectroscopy (fNIRS) is a powerful tool for the study of oxygenation and hemodynamics of living tissues. Despite the continuous nature of the processes generating the data, analysis of fNIRS data has been limited to discrete-time methods. We propose a technique, namely functional data analysis (fDA), that converts discrete samples to continuous curves. We used fNIRS data collected on forehead during a cold pressor test (CPT) from 20 healthy subjects. Using functional principal component analysis, oxyhemoglobin (HbO2) and deoxyhemoglobin (Hb) curves were decomposed into several components based on variability across the subjects. Each component corresponded to an experimental condition and provided qualitative and quantitative information of the shape and weight of that component. Furthermore, we applied functional canonical correlation analysis to investigate the interaction between Hb and HbO2 curves. We showed that the variation of Hb and HbO2 was positively correlated during the CPT, with a "far" channel on right forehead showing a smaller and faster HbO2 variation than Hb. This research suggests the fDA platform for the analysis of fNIRS data, which solves problem of high dimensionality, enables study of response dynamics, enhances characterization of the evoked response, and may improve design of future fNIRS experiments.