To facilitate the analysis of frequency-structure correlations in the amide I vibrational spectroscopy of proteins, we investigate visualization methods and spatial correlation functions that describe delocalized vibrations of proteins and protein secondary structures. To study those vibrational modes revealed in infrared spectroscopy, we characterize frequency-dependent bright states obtained from doorway mode analysis. Our visualization methods pictorially color code amplitude and phase of each oscillator within the structure to reveal spatially varying patterns characteristic of excitations within sheets and helices. Spatial correlation functions in the amplitude and phase of amide I oscillators quantitatively address the extent of delocalization and the alpha helical and beta sheet character of these modes. Specifically, we investigate the vibrations of idealized antiparallel beta sheets and alpha helices and perform case studies on three proteins: concanavalin A, myoglobin, and ubiquitin.