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The theory of the transmission of digital data by frequency-shift methods has recently aroused new interest as a result of the increased requirements for frequency band conservation in telemetering and pulse-code modulation (PCM) applications. Assuming random 8equences of binary FM signals in the form of two equally probable, alternative frequencies for "mark" and "space" with continuous phase transition, the power density spectrum for a large ratio of carrier frequency to bit rate has been derived in closed mathematical form. As one of the surprising results it has been noted that a peak to peak deviation of about 0.6 to 0.7 times the bit ratlee ads to a particularly efficient crowding of the spectrum near the carrier frequency, resulting in a high efficiency of transmission in terms of occupied bandwidth. For many applications a quantitative expression for the cumulative band occupancy is needed which can be derived by integration of the power density function, and evaluation in terms of percentage of total signal power within given band limits. The following covers the results of auch an integration together with an assessment of the effects of pre- and postmodulation band limitation with linear phase Gaussian response filters. As one of the main conclnsions to be drawn from the calculations presented, it is found that in conventional digital FM transmission 99% of the signal power can be confined within a total bandwidth of 1.1 to 1.2 times the bit rate if the peak to peak deviation is kept below a maximum value between 0.6 and 0.7 times the bit rate, depending on the amount of pre- and postmodulation filtering.