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This paper treats the bandwidth properties and optimum demodulation of single-sideband FM. Bandwidth is defined as the second central moment of the power spectrum. With this definition, a comparison is given between FM and SSBFM signals for modulating sinusoids, and it is shown that a reduction in bandwidth can be obtained over FM with SSBFM. The a posteriori most probable demodulator for SSBFM is derived on the assumption of Gaussian modulating signals and is shown to combine some of the features of both optimum amplitude and angle demodulation.