Using the Huygens-Fresnel diffraction integral and the Fourier transform, the propagation representations of pulses with Hermite-Gaussian transverse modes passing through a hard-edged aperture are derived. Influences of the bandwidth on the transverse intensity distributions are analyzed in detail from numerical calculations. It is found that lots of intensity spikes emerge and the near field intensities are non-uniformity when the pulses pass through the aperture. However, when the bandwidth increases, the number and the amplitude of the spikes are reduced and thus the beam uniformity is improved, the intensity spike does not appear in the far field, and also the beam width decreases in the far field. Therefore, the smoothing and narrowing effects can be brought forth by increasing the bandwidth. In addition, it is found from the numerical results that the effects are similar in the pulses with Hermite-Gaussian transverse modes of mode indices 1 and 2.