A number of papers have appeared during recent years about electromagnetic waves produced by antenna currents with the time variation of Walsh functions rather than that of sinusodial functions. Experimental transmitters and receivers for such waves have been developed. There are a variety of effects of Walsh waves that do not exist for sinusoidal waves or are so obscure that they are generally not recognized. This makes a discussion of these effects difficult for the nonspecialist. The range-Doppler resolution in radar lends itself more readily to a discussion, since Walsh waves bring in this case not a new effect, but only a substantial improvement of a well-known one. It is shown that our present technology should permit an improvement of about one order of magnitude in the Doppler resolution by using carriers derived from Walsh or other two-valued functions rather than sinusoidal functions. The theoretical improvement of the relative range resolution is substantially greater since it no longer depends upon the duration of the modulating signal but upon the period of the carrier and the switching time of the carrier. The absolute range measurement is not changed.