This paper gives a straightforward method of obtaining an explicit expression for the spectrum of a correlative encoded digital FM signal. An investigation of the band occupancy for various encoding schemes with rectangular, as well as raised-cosine pulse shaping, is carried out. Correlative encodings that are spectrally more efficient than minimum shift keying (MSK) and that promise an improved error performance are shown. In addition, if a small degradation in error performance is tolerated, substantial increases in band efficiency are possible. For example, with the polynomial(1 + 2D + D^{2})/4the signal is spectrally 47 percent more efficient than MSK and with an SNR performance degradation of only 1.1 dB.

This paper presents a technique for optimizing the baseband pulse shapes in digital angle modulated signals to minimize the fraction of out-of-band power for a given channel bandwidth. As examples of practical interest, the optimization is carried out for channel bandwidths up to three times the bit rate and for the range of modulation indices usually encountered in digital transmission. Results for MSK-type signals appear as a special case.