Signal-detection tradeoff-analysis of optical vs digital Fourier transform computers

Signal detection theory is used to develop analytic models which yield comparisons between optical and digital Fourier transform computers in terms of their ability to detect transformed signals within small spectral regions of their Fourier domains. Stochastic noise models are first given describing the quantization noise introduced by the finite register length involved in a digital transformation. The signal detection models are then developed which describe the detectability of a transformed signal among this kind of noise, with models given for fixed-point and floating-point machines and for the signal-known-exactly and the signalunknown detection cases. These models provide the optimum detection statistic to be used in each case, a means for choosing the cutoff points used in the detection process, the over-all performance curve of the detector, and detection indices which summarize this performance. The optical and digital computers are compared by equating their detectabilities as obtained from these models, thus allowing a digital processor with given specifications to be paired with an optical processor with a specific SNR in its output plane. Analytical results are presented demonstrating these comparisons in which computer number-representation, register length, transform-array size, detection-array size, and type of detection are the independent variables under consideration.