An investigation of the spectra of binary frequency-modulated signals with various build-up waveforms

It is found that a straight-line waveform is the best that can be employed for the transition between mark and space frequencies in frequency-shift radiotelegraphy, since this waveform involves the minimum occupied bandwidth for a given total build-up time. Data on the spectra of frequency-shift signals using straight-line build-up, i.e. a trapezoidal waveform, are presented for modulation indices between 1 and 6 and build-up times between 0 and 0.31 of a telegraph element. Although the work was initiated for radiotelegraphy, the results are, of course, applicable to frequency-modulated signals generally.