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This paper first describes the phenomenon of Gaussian pulse spread due to numerical dispersion in the finite-difference time-domain (FDTD) method for electromagnetic computation. This effect is undesired, as it reduces the precision with which multipath pulses can be resolved in the time domain. The quantification of the pulse spread is thus useful to evaluate the accuracy of pulsed FDTD simulations. Then, using a linear approximation to the numerical phase delay, a formula to predict the pulse duration is developed. Later, this formula is used to design a Gaussian source that keeps the spread of numerical pulses bounded in wideband FDTD. Finally, the developed model and the approximation are validated via simulations.