Blood Oxygen Level-Dependent (BOLD) time course in functional magnetic resonance imaging (fMRI) is modeled as the response of the hemodynamic response function (HRF) excited by an activity-inducing signal. Variability of the HRF across the brain influences functional connectivity (FC) estimates and some approaches have been attempted to separate the HRF and activity-inducing signal from the observed BOLD signal as a blind separation problem. In this work, an approach based on homomorphic filtering is proposed to estimate a non-parametric representation of HRF in resting state fMRI. Voxel-wise and region-wise variations of correlation of the estimated HRF (both the parametric and non-parametric representation) are analyzed in different functional networks. Principal component analysis of the correlation matrix using the estimated HRF is used to analyze the interconnectedness. HRF shows higher variability for the non-parametric representation over the parametric representation. Further, the contribution of the estimated HRF is then studied in producing resting-state networks using the dictionary learning framework.