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The efficiency as measured by data rate per unit bandwidth of certain digital modulation systems is compared. The systems considered are frequency modulation (FM), phase modulation (PM), and linear modulation. The achievable bits per cycle in digital PM and amplitude modulation (AM) at a given signal-to-noise ratio and error rate have been known for some time. In digital FM this quantity can be maximized, a fact apparently first realized by J. R. Pierce at Bell Telephone Laboratories. Rigorous optimizations were later carried out by Mazo, Rowe, and the author. In addition to the comparisons made with other systems, additional details related to the optimization problem in frequency-shift keying (FSK) are also furnished. Whereas previous treatments analyzed a frequency discrimination system, this paper treats the optimum detector. The results indicate very minor differences m efficiency attained by the two different models analyzed. Results are exhibited graphically, showing the relationships between the important system parameters.