The representation of signals

As the communication art becomes more sophisticated, engineers are being called on to deal more and more with complicated signals. This trend is typified by the use of noise-like signals to combat multipath (as in the RAKE), various suggestions for improving the range and velocity resolution of radars, and the desire to evolve ways of reducing the complication of a signal (as in the case of narrow band coding schemes for speech). As yet, however, no set of analytical tools has been developed which make the behavior of such complicated signals both easy to compute and simple to understand. This paper reviews some of the techniques which have been evolved for dealing with signals, and the difficulties that arise in using them; it then generalizes a unit-function procedure first suggested by Gabor into flexible procedure for picturing and computing the behavior of complicated signals.