Minimum shift keying (MSK)-type signals, while possessing all the advantages of MSK, allow input data pulse shaping in order to obtain more desirable spectral behavior. This paper presents a set of conditions on the pulse shape which enable an MSK-type signal to have a fast spectral rolloff. An

th order shaping function, resulting in an asymptotic spectral falloff as

, is presented. Previously considered schemes such as MSK and sinusoidal frequency shift keying (SFSK) are shown to be special eases of this shaping function.