When it comes to the high-spatial-frequency electromagnetic waves, we usually think of them as the evanescent waves which are bounded at the near-field surface and decay along with propagation distance. A conventional wisdom tells us that the high-spatial-frequency waves cannot exist in the far field. In this work, we show, however, that these high-spatial-frequency waves having wavenumbers larger than the incident one can propagate freely to the far-field regions. We demonstrate theoretically a technique, based on an abrupt truncation of the incident plane wave, to generate these intriguing waves. The truncation functions describing the slit and the complementary slit are considered as typical examples. Our results show that both the slit structures are able to produce the high-spatial-frequency wave phenomena in the far field, manifested by their interference fringes of the diffracted waves. This work introduces the high-spatial-frequency propagating waves. Therefore, it may trigger potential investigations on such an interesting subject, e.g., one may design delicate experiment to confirm this prediction. Besides, it would stimulate potential applications such as in superresolution and precise measurement.