The idea of using the dynamical behaviour of a semiconductor laser to perform a certain processing operation of an input signal has been around for quite a long time. While the unidirectional optical injection scheme seems well suited to such a target-with the injection serving as an optical carrier for the input signal-the impact of a modulation of the injection beam still requires thorough investigation. Here, we study the case of an optically injected laser with a simple single-tone modulation term added to the injection signal. We analyse the impact of amplitude modulation on the laser dynamics, and particularly focus on the evolution within the injection locking range. We highlight clear passband behaviour corresponding to the laser resonance at its relaxation oscillation frequency, and characterize its features for various parameter changes. Next, we report dramatic differences between amplitude and phase modulation as the latter quickly leads to a loss of the injection locking and to the emergence of chaotic dynamics in place from the passband response identified in the case of amplitude modulation. At last, we discuss the suitability of using laser diodes for signal filtering, as was recently proposed by others, and identify the main remaining issues that need to be overcome.