This paper describes a wideband synthetic-aperture system and the associated Fourier processing for generating high-resolution spatial and temporal estimates of the signal propagation environment in wireless communication channels at millimeter-wave frequencies. We describe how to configure the synthetic aperture system for high angular resolution by sampling the progression of signal phase across a large planar area in space. We also show how to synthesize discrete measurements of the channel frequency response taken sequentially over a wide bandwidth to create power delay profiles (PDPs) in specified angular directions with high delay resolution. We provide a rigorous uncertainty analysis that can be made metrologically traceable to fundamental physical standards. This uncertainty framework can propagate the errors inherent in the measured signals through to the final channel estimates and derived parameters such as root-mean-square delay or angular spread. We illustrate use of the system in conjunction with two different analysis tools to extract both narrowband and wideband parameter estimates from the synthetic aperture, allowing its use as a stand-alone channel sounder or as a tool for verifying the performance of wireless devices.