Antenna near fields can be accurately computed by the plane wave spectrum (PWS) method. The PWS is directly related to the far field at infinity. That is, at infinity, only a single plane wave contributes to the field. At the close-in distance of just a few wavelengths away from the antenna, integration is performed over all visible wavenumbers and some evanescent wavenumbers. Close (less than a wavelength) to the antenna, integration is performed over all wavenumber space. In between these two extreme distances from the antenna, there is shown to be a finite-sized subregion of all wavenumber space that contains all significant contributions to the field. That is, near fields are shown to be wavenumber-bandwidth-limited. Exploiting this fact, a technique of computing near fields could be created which is faster than both the aperture method and the original PWS method, once a suitable method is developed for determining the wavenumber bandwidth of near fields.