The authors investigate the propagation of picosecond pulses through Semiconductor Optical Amplifiers using the measurement technique of Frequency Resolved Optical Gating by applying pulses of varying peak power, pulse width and shape. Frequency Resolved Optical Gating is a relatively new measurement system which provides complete characterisation of the pulses in both the temporal and spectral domains. We examine the pulses before and after amplification through the Semiconductor Optical Amplifier. The work shows pulse broadening, the formation of large pulse pedestals, and the generation of significant frequency chirp across the pulse in the temporal domain. In the spectral domain results exhibit spectral broadening and a shift to longer wavelengths. These properties of the output pulses would cause serious degradation in high-speed communications systems employing Wavelength Division Multiplexing and Optical Time Division Multiplexing. The resulting physical properties occurring to the pulses due to propagation through the Semiconductor Optical Amplifier are a result of Self Phase Modulation, which is due to gain saturation induced by carrier depletion and carrier heating.