On the Spectral Properties of Single-Sideband Angle-Modulated Signals

Among the more recent signal transmission techniques for conserving spectral bandwidth is single-sideband angle modulation, first proposed and investigated by Bedrosian.1 In this scheme a carrier wave is simultaneously angle modulated by an appropriate baseband (bandlimited) signal and amplitude modulated (multiplied) by the negative exponential of the Hilbert transform of the baseband signal, the combined modulation process resulting in an RF spectrum which vanishes identically on the low-frequency side of the carrier frequency and carrier axis crossings which coincide exactly with those of a conventional angle-modulated carrier modulated by the same baseband signal. The single-sideband and axis-crossing properties, although suggesting means with which to obtain ideal bandwidth reduction and compatible detection, are only partially applicable to physical systems.* In general, the RF spectra under the combined and conventional modulation schemes are of infinite extent, and the nonvanishing portion of the spectrum under the former can have, according to any one of several common definitions, a larger effective bandwidth than that under the latter; consequently, single-sideband angle modulation does not necessarily lead to bandwidth reduction, and * Detection compatibility is suggested by the fact t h a t the output of an ideal limiter depends only 011 the axis crossings of the input. 2811