The magnetar 1E 1547.0-5408 exhibited outbursts in 2008 October and 2009 January. In this paper, we present in great detail the evolution of the temporal and spectral characteristics of the persistent total and pulsed emission of 1E 1547.0-5408 between ~1 and 300 keV starting on 2008 October 3 and ending in 2011 January. We analyzed data collected with the Rossi X-ray Timing Explorer (RXTE) the International Gamma-Ray Astrophysics Laboratory (INTEGRAL), and the Swift satellite. We report the evolution of the pulse frequency, and the measurement at the time of the onset of the 2009 January outburst of an insignificant jump in frequency, but a major frequency derivative jump Delta {dot{nu }} of +(1.30 ± 0.14) × 10-11 Hz s-1 (Delta dot{nu }/dot{nu } of -0.69 ± 0.07). Before this dot{nu } glitch, a single broad pulse is detected, mainly for energies below ~10 keV. Surprisingly, ~11 days after the glitch a new transient high-energy (up to ~150 keV) pulse appears with a Gaussian shape and width 0.23, shifted in phase by ~0.31 compared to the low-energy pulse, which smoothly fades to undetectable levels in ~350 days. We report the evolution of the pulsed-emission spectra. For energies 2.5-10 keV all pulsed spectra are very soft with photon indices Γ between -4.6 and -3.9. For ~10-150 keV, after the dot{nu } glitch, we report hard non-thermal pulsed spectra, similar to what has been reported for the persistent pulsed emission of some anomalous X-ray pulsars. This pulsed hard X-ray emission reached maximal luminosity 70 ± 30 days after the glitch epoch, followed by a gradual decrease by more than a factor of 10 over ~300 days. These characteristics differ from those of the total emission. Both, the total soft X-ray (1-10 keV) and hard X-ray (10-150 keV) fluxes, were maximal already 2 days after the 2009 January outburst, and decayed by a factor of gsim3 over ~400 days. The total spectra can be described with a blackbody (kT values varying in the range 0.57-0.74 keV) plus a single power-law model. The photon index exhibited a hardening (~ – 1.4 to ~ – 0.9) with time, correlated with a decrease in flux in the 20-300 keV band. We discuss these findings in the framework of the magnetar model.
