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Distortions caused by system components and by fundamental physical phenomena can limit the performance of photonic time-stretch ADCs. Here we use a combination of time-stretch linearization & equalization, DC-offset subtraction, and operation in a linear propagation regime to improve the signal-to-noise-and-distortion ratio by 17 dB for a 2-channel time-stretch ADC testbed and therein obtain noise-limited performance of 6-7 ENOB over a 10-GHz RF input bandwidth. Time-stretch linearization & equalization corrects for dispersion mismatches among testbed components by applying time-shifts calculated from component group delays to output ADC samples. DC-offset subtraction removes static errors due to insertion loss imbalances and Mach-Zehnder modulator bias offsets. If optical power levels are too high, nonlinear fiber propagation lowers the frequencies of dispersion-induced nulls in the RF transfer function and causes higher-order signal distortions. The 2-channel testbed can be directly scaled to a practical continuous-time system with the addition of more sub-aperture wavelength channels (total of 13 channels and 42 nm of optical bandwidth for a 90 MHz laser repetition rate). Adaptive online and fixed pre-calibrated stitching methods are demonstrated for joining data from one wavelength channel to the next.