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Swept coherent optical spectrum analysis is becoming a viable method for subpicometer spectral characterization of optical communications signals. The performance of this technique depends on a number of factors that we have investigated both theoretically and experimentally. This includes the influence of signal linewidth, polarization, optical phase, intensity noise, and electrical filtering methods. These effects are discussed in detail and illustrated through spectral measurements on communications transmitters. We extend the heterodyne method to permit measurement of both spectral amplitude and phase of the spectral sidebands. The transformation of the complex optical field spectrum to the time domain waveform is demonstrated.