Associated particle imaging (API) is a non-destructive nuclear technique for the 3D determination of isotopic distributions. By detecting the alpha particle associated with the emitted neutron in the deuterium-tritium fusion reaction with a position- and time-resolving detector, the direction of the 14.1 MeV neutron and its time of emission can be determined. Employing this method, isotope characteristic gamma rays emitted in inelastic neutron scattering events can be correlated with the neutron interaction location. An API system consisting of a sealed-type neutron generator, gamma detectors, and a position-sensitive alpha detector was designed, constructed, and characterized. The system was tested with common soil elements and shown to be sensitive to 12C, 16O, 28Si, 27Al, and 56Fe. New aspects of our approach are the use of a yttrium-aluminum-perovskite scintillator, using a sapphire window instead of a fiber-optic faceplate for light transport to the photomultiplier, and the all-digital data acquisition system. We present a description of the system with simulations and experimental results that show a position resolution on the alpha detector of 1 mm, a depth resolution using a LaBr3 detector of 6.2 cm, and an angular resolution of 4.5°. Additionally, we present single-element gamma response measurements for the elements mentioned above together with a comparison to Monte Carlo simulations (MCNP6).