Line mixing effects have been studied in the nu(2) and nu(1) parallel bands of NH3 perturbed by He at room temperature. Experiments have been made with a Fourier transform spectrometer covering a wide range of total pressures up to about 400 atm. Analysis of the spectra demonstrates, for the first time, that the spectral shapes of entire ammonia bands can be significantly influenced by line mixing. A theoretical approach based on the energy corrected sudden approximation (ECS) is used to predict and analyze these effects. The model parameters include dynamical factors directly computed from an NH3-He potential energy surface and a scaling length which has been determined from a fit of line-broadening data. Comparisons with measurements show that the ECS model leads to surprisingly satisfactory predictions when considering the large spacing between rotational levels. The large effects of line mixing within the Q branches and in the far wing of the absorption bands are analyzed. It is shown that purely Lorentzian calculations can lead to underestimation of the Q branch peak by a factor of up to 4, whereas the overestimation of absorption in the band wing reaches one order of magnitude. On the contrary, the proposed ECS approach leads to much better results and accounts for most of the transfers of intensity among the various spectral components. It is used for the analysis of the shape of Q branches, P and R manifolds and line wings. Remaining discrepancies are discussed in terms of the model approximations and the improper dependence of the basis dynamical factors on quantum numbers induced by uncertainties on the potential energy surface used.