Closed-form of the power spectral density for full response M -ary CPFSK modulation

A special method of analyzing the spectral properties of M-ary CPFSK (continuous-phase frequency shift keying) for full response signaling is presented. The autocorrelation function is presented in closed form, thereby avoiding truncation. A new transient component of the autocorrelation function is reported. The Fourier transform is used to find the power spectral density (PSD) function, which is also expressed in closed form. The effects of the system parameters, i.e., the M size of the alphabet, the modulation index, etc., on the system bandwidth and PSD are analyzed. The conditions under which the spectrum contains discrete lines are outlined. The continuous part of PSD is expressed in exponential form. A large number of PSDs have been computed and plotted in a relatively short time and are presented. Interesting results about both PSD and bandwidth are obtained for different choices of system parameters