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Coherent optical systems, which utilize the wave nature of light and the consequent diffraction phenomena, may often be used to supplement or even replace complex electronic equipment. Such systems are particularly adapted to the performance of certain linear mathematical operations, particularly those of an integral transform nature such as spectral analysis, convolution, auto- and cross-correlation, and matched filtering. The two-dimensional nature of optical systems, contrasted with the inherent one-dimensional nature of an electronic channel, allows a great reduction in equipment complexity for certain classes of operations. This paper discusses the theory behind optical channels and filters as outlined above, and also illustrates simple multi-channel optical systems which can carry out representative operations.