© 2016 IOP Publishing Ltd. Objective. Electrocorticography (ECoG) has become an important tool in human neuroscience and has tremendous potential for emerging applications in neural interface technology. Electrode array design parameters are outstanding issues for both research and clinical applications, and these parameters depend critically on the nature of the neural signals to be recorded. Here, we investigate the functional spatial resolution of neural signals recorded at the human cortical surface. We empirically derive spatial spread functions to quantify the shared neural activity for each frequency band of the electrocorticogram. Approach. Five subjects with high-density (4 mm center-to-center spacing) ECoG grid implants participated in speech perception and production tasks while neural activity was recorded from the speech cortex, including superior temporal gyrus, precentral gyrus, and postcentral gyrus. The cortical surface field potential was decomposed into traditional EEG frequency bands. Signal similarity between electrode pairs for each frequency band was quantified using a Pearson correlation coefficient. Main results. The correlation of neural activity between electrode pairs was inversely related to the distance between the electrodes; this relationship was used to quantify spatial falloff functions for cortical subdomains. As expected, lower frequencies remained correlated over larger distances than higher frequencies. However, both the envelope and phase of gamma and high gamma frequencies (30-150 Hz) are largely uncorrelated (<90%) at 4 mm, the smallest spacing of the high-density arrays. Thus, ECoG arrays smaller than 4 mm have significant promise for increasing signal resolution at high frequencies, whereas less additional gain is achieved for lower frequencies. Significance. Our findings quantitatively demonstrate the dependence of ECoG spatial resolution on the neural frequency of interest. We demonstrate that this relationship is consistent across patients and across cortical areas during activity.