During the last few years, large-scale efforts towards realizing high-photonic integration densities have put SOAs in the spotlight once again. Hence, the need to develop a complete framework for SOA-induced signal distortion to accurately evaluate a system's performance has now become evident. To cope with this demand, we present a detailed theoretical and experimental investigation of the deterministic timing jitter and the pulse peak power equalization of SOA-amplified intensity-modulated optical pulses. The deterministic timing jitter model relies on the pulse mean arrival time estimation and its analytic formula reveals an approximate linear relationship between the deterministic timing jitter and the logarithmic values of intensity modulation when the SOA gain recovery time is faster than the pulse period. The theoretical analysis also arrives at an analytic expression for the intensity modulation reduction (IMR), which clearly elucidates the pulse peak power equalization mechanism of SOA. The IMR analysis shows that the output intensity modulation depth is linearly related to the respective input modulation depth of the optical pulses when the gain recovery time is faster than the pulse period. This novel theoretical platform provides a qualitative and quantitative insight into the SOA performance in case of intensity-modulated optical pulses.