(Abridged) We present numerical simulations of the spectral evolution and emission of radio components in relativistic jets. We have developed an algorithm (SPEV) for the transport of a population of non-thermal electrons including radiative losses. For large values of the ratio of gas pressure to magnetic field energy density, ab sim 6times 10^4, quiescent jet models show substantial spectral evolution, with observational consequences only above radio frequencies. Larger values of the magnetic field (ab sim 6times 10^2), such that synchrotron losses are moderately important at radio frequencies, present a larger ratio of shocked-to-unshocked regions brightness than the models without radiative losses, despite the fact that they correspond to the same underlying hydrodynamic structure. We also show that jets with a positive photon spectral index result if the lower limit gamma_min of the non-thermal particle energy distribution is large enough. A temporary increase of the Lorentz factor at the jet inlet produces a traveling perturbation that appears in the synthetic maps as a superluminal component. We show that trailing components can be originated not only in pressure matched jets, but also in over-pressured ones, where the existence of recollimation shocks does not allow for a direct identification of such features as Kelvin-Helmholtz modes, and its observational imprint depends on the observing frequency. If the magnetic field is large (ab sim 6times 10^2), the spectral index in the rarefaction trailing the traveling perturbation does not change much with respect to the same model without any hydrodynamic perturbation. If the synchrotron losses are considered the spectral index displays a smaller value than in the corresponding region of the quiescent jet model.
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