A joint research program at the universities of Arizona and Massachusetts (Medical school) is designing a next-generation, adaptive, dedicated brain-imaging, single photon emission computed tomography (SPECT) system. It consists of multi-pinhole, modular gamma cameras arrayed around a hemisphere that encloses the volume of interest. The adaptive feature of the system stems from the capability of shuttering selected pinholes for each module. Critical to the design process is the ability to vary parameters such as the number, location and size of the pinholes and quantify their effects on system performance. One approach is to use the Fourier-crosstalk matrix (FXM) which is derived from the system matrix and can provide a modulation transfer function (MTF)-type measure of system resolution. An FXM-based study has been initiated to answer some of the questions regarding pinhole/detector placement in the proposed SPECT system. The initial work has entailed obtaining system matrices for individual detector modules and then deriving the FXM from it (via a multidimensional discrete Fourier transform (DFT)).