  We investigate the spectral degree of freedom of OAM-carrying localized
waves, and its influence on their transverse intensity distribution. In
particular, we focus our attention on two different families of spectra, namely
exponentially decaying spectra, which are very tightly connected to fundamental
X-waves, and Bessel-modulated spectra. For each class we show how it is
possible, by suitable manipulating their spectrum, to structure their
transverse intensity distribution, thus creating a radial structure similar to
that of Laguerre-Gaussian beams. To complete our analysis, we investigate the
impact of the two spectral functions on linear and angular momentum of such
localized waves.
