In this study, ceramic samples of lead zirconate titanate Pb(Zr0.42Ti0.58)O3 (PZT 42/58) doped with Fe (hard) and Nb (soft) were studied by Raman, infrared (IR) and THz spectroscopy in the temperature range from 900 to 20 K. From the evaluation of the IR and Raman phonons in undoped ceramics, we conclude that tetragonal PZT ceramics undergo a low-temperature phase transition to a tilted phase, revealed by anomalies in phonon parameters and the appearance of new modes. Doped samples also presented similar behaviour. The main differences between undoped and doped ceramics lie in the dielectric behaviour below phonon frequency range, where several mechanisms appear: a soft central mode (CM) located near 1 THz and two relaxations in the GHz range. Both types of doping raise the permittivity values below the phonon frequencies, not only increasing the dielectric contribution of the CM, but also modifying the dielectric response near the GHz range. Soft ceramics show higher permittivity with logarithmic increase at low frequencies, corresponding to an almost frequency-independent value of the dielectric losses below 0.1 GHz.