An analysis of the detection of repeated signals in noise by binary integration

An analysis of the detection of repetitive signals in noise by binary integration techniques is made. An expression for the effective signal-to-noise ratio of the quantized video is obtained and is shown to apply to any half-wave second detector. A comparison of analog and digital integration is made, and it is further shown that digital integration is, at most, 1.9 db poorer due to the quantization loss. However, the loss due to nonideal analog integration can make the two types equivalent. The optimum settings for quantizer and counter thresholds are derived, and expressions for the final-detection and false-alarm probabilities are determined. Lastly, the results are modified to include the effect of nonuniform amplitudes in the set of signals being quantized and integrated.