The ability to perceive speech is related to the listener's ability to differentiate among frequencies (i.e. spectral resolution). Cochlear implant users exhibit variable speech perception and spectral resolution abilities, which can be attributed at least in part to electrode interactions at the periphery (i.e. spatial resolution). However, electrophysiological measures of peripheral spatial resolution have not been found to correlate with speech perception. The purpose of this study was to systematically evaluate auditory processing from the periphery to the cortex using both simple and spectrally complex stimuli in order to better understanding the underlying processes affecting spatial and spectral resolution and speech perception. Eleven adult cochlear implant users participated in this study. Peripheral spatial resolution was assessed using the electrically evoked compound action potential (ECAP) to measure channel interaction functions for thirteen probe electrodes. We evaluated central processing using the auditory change complex (ACC), a cortical response, elicited with both spatial (electrode pairs) and spectral (rippled noise) stimulus changes. Speech perception included a vowel-discrimination task and the BKB-SIN test of keyword recognition in noise. We varied the likelihood of electrode interactions within each participant by creating three experimental programs, or MAPs, using a subset of seven electrodes and varying the spacing between activated electrodes. Linear mixed model analysis was used to account for repeated measures within an individual, allowing for a within-subject interpretation. We also performed regression analysis to evaluate the relationships across participants. Both peripheral and central processing abilities contributed to the variability in performance observed across CI users. The spectral ACC was the strongest predictor of speech perception abilities across participants. When spatial resolution was varied within a person, all electrophysiological measures were significantly correlated with each other and with speech perception. However, the ECAP measures were the best single predictor of speech perception for the within-subject analysis, followed by the spectral ACC. Our results indicate that electrophysiological measures of spatial and spectral resolution can provide valuable information about perception. All three of the electrophysiological measures used in this study, including the ECAP channel interaction functions, demonstrated potential for clinical utility.