The optical convolution of time functions

The ease with which an optical system can achieve an extremely large time-bandwidth product makes optical filters and cross-correlation function generators attractive for signal detection and parameter estimation when signal-to-noise ratios are very low. The principles of a new optical filter that overcomes the sometimes severe positioning requirements of conventional optical filters are described. The relationship between the signal amplitude and matched-filter impulse response amplitude is discussed, and a method for reducing a noise component that is common to all optical filters is given. A matched filter was constructed and used to detect a radar-like pulse when the signal-to-noise ratio was -40 dB. A digital computer may be used with an optical system to filter time signals with an accuracy that potentially is as good as the accuracy of an all-digital system, but with a significant reduction in computation. The theory of an optical digital filter is presented.