Abstract: The far-field anomalous spectral behaviors of a Gaussian pulsed beam passing through a linear circular apertures array are studied. By expanding a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral intensity of a space-time-dependent Gaussian pulsed beam passing through a linear circular apertures array is derived. The red and blue shifts and the spectral intensity distribution are studied and illustrated with numerical calculations. It is shown that there exist spectral switches when the observation position is at the right points.