Gain-saturation-induced self-phase modulation (SPM) leading to pulse distortion in a semiconductor optical amplifier (SOA) is overcome by shifting a tunable optical filter (TOF). A recovered or broadened pulse can be obtained after filtering the amplified pulse in the SOA even if the short pulse is only 2-3 ps long. The input power dynamic range (IPDR) can be strongly increased by shifting the TOF and the direction of the shifted transparent wavelength is different for 10 Gb/s return-to-zero (RZ) or nonreturn-to-zero (NRZ) signals. The transparent wavelength of the TOF should be shifted to a longer wavelength for RZ signals and to a shorter for NRZ signals. 80-Gb/s optical time division multiplexing (OTDM) signal amplification in the SOA is demonstrated for the first time. We also demonstrate that a large IPDR for the 80-Gb/s OTDM signal can be obtained by shifting the TOF.