Optimum combination of pulse shape and filter to produce a signal peak upon a noise background

The paper concerns the generation of a signal pulse for transmission through a propagating medium and its subsequent detection as a single peak after it is received upon a noise background. It is supposed that the propagating medium behaves as a linear filter and that the noise background is independent of the signal. The pulse is conveniently described as consisting of a central portion attached to a leading edge and a trailing edge. It is found that for a given length of central portion there is an optimum combination of transmitted pulse shape and predetection filter. The results are compared with those arising from the use of certain non-optimum systems, and it is found that the optimum system leads to a significantly high signal/noise ratio. The results of the paper imply that for the range of parameters considered it is advantageous to transmit a succession of short pulses of a determined form rather than a single smooth pulse.