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The time-bandwidth product of the photonic time-stretched system is modeled in terms of physical system parameters. Using the time-bandwidth product as figure-of-merit, the performances of optical double-sideband and single-sideband (SSB) intensity modulation are compared, and optical SSB intensity modulation is identified as a potential solution to extend the system's time-bandwidth product. An SSB-modulated time-stretched system is theoretically analyzed and experimentally demonstrated. As an important practical consideration, the analytical model relating the system performance to the phase and amplitude mismatches in the SSB modulator is presented. The results show that the system is tolerant to such unavoidable mismatches. Experiments using commercially available components suggest that the dispersion-induced power penalty can be kept below 2.5 dB over 4 - 20 GHz bandwidth for any stretch factor. Additional experiments demonstrating 120-GSamples/s real-time digitization of a 20-GHz SSB-modulated signal are also reported.