Spectra of CPFSK signals with modulation pulse shaping

An analysis is made of the spectra of CPFSK signals with various forms of modulation pulse shaping, even different from the rectangular form and, in any case, strictly time-limited to an interval with a duration not exceeding the symbol time. It is shown that, for different modulating waveforms, the main lobe in the signal spectrum depends only slightly on the actual shape of the modulating waveform, whereas it depends substantially on the maximum phase deviation in a symbol interval. In the multilevel case, no appreciable changes in the spectral density are obtained by varying the intermediate modulation levels. It is noted that the present results will make it possible to give an intuitive interpretation of the performance requirements that can be obtained by an appropriate exploitation of the degrees of freedom in the transmitted signal both in normal propagation conditions and during multipath fading.