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We report the first quantitative study of intensity noise induced in line-by-line pulse shaping in response to time-varying changes in the comb frequency offset. Controllable comb linewidth broadening is synthesized through frequency dithering of a continuous-wave laser that is fed to a phase modulator. An electrical spectrum analyzer is used to examine the current power spectra of shaped time-domain intensity waveforms subject to comb frequency noise. A theoretical model predicting a 20 dB/decade scaling relation between the dither-induced noise and the frequency dither amplitude is presented. A numerical simulation method capable of predicting the precise form of the RF power spectrum in the presence of optical frequency dithering is explained. Two line-by-line shaping cases are considered in detail. Experimental data are in excellent agreement with the simulated results down to frequency dithers of a few tenths of a percent of the comb spacing. Tolerances to laser frequency fluctuations are given for several simple pulse shaping examples. The effect of pulse shaper parameters is also discussed.