Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital–optical equivalents of such systems could be built that share many features of the analog systems while allowing greater accuracy. We show that the digital equivalent of any system consisting of an arbitrary number of lenses, filters, spatial light modulators, and sections of free space can be constructed. There are many possible applications for such systems as well as many alternative technologies for constructing them; this paper stresses the potential of free-space interconnected active-device-plane-based optoelectronic architectures as a digital signal processing environment. Implementation of the active-device planes through hybridization of optoelectronic components with silicon electronics should allow the realization of systems whose performance exceeds that of purely electronic systems.