The spectral structure of the reflected and transmitted fields due to a three dimensional electromagnetic X-wave incident on a planar air-dielectric interface is examined. Using a novel superposition of azimuthally dependent pulsed plane waves, it is shown that for oblique incidence the reflected pulse has a localized wave structure. On the other hand, the transmitted field maintains its localization up to a certain distance from the interface beyond which it starts disintegrating. A study of the effects of polarization on the amplitudes of the reflected and transmitted wave fields is presented.