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We describe the numerical analysis of a lightwave synthesized frequency sweeper (LSFS) that uses an optical single-sideband (SSB) modulator composed of four optical phase modulators. The SSB modulator realizes a large frequency shift in the LSFS. This means that we can reduce the number of pulse circulations in the LSFS cavity to cover a given frequency sweep range. We propose a frequency-domain analysis method for the LSFS, in which a general optical modulator is expressed by using a matrix that includes optical phase terms. We employ this method to simulate the LSFS for several different phaseand group-velocity dispersion values in the lightpaths in the LSFS cavity. The results indicate that we can realize a linear frequency sweep by adjusting the phase change of the modulation signal during the cavity round-trip time.