Optical systolic processors perform rapid parallel multiplications of vector and matrix elements. These multiplications may be performed by convolving the digits of individual numbers. Current transducers (particularly acousto-optic cells) make time-domain convolution the method of choice. A time-domain convolver can operate in time-integrating or space-integrating modes. These two modes can be considered as variations of a basic multiplier unit. Starting with the basic multiplier, four matrix-vector and two matrix-matrix multipliers can be derived. Some of these processors are new, and some have been previously identified. Within this unifying framework the perfor-mance of all these processors may be analyzed, and design trade-offs may be identified.