In this paper, we report a study of the features of polarized and unpolarized narrow-band amplified spontaneous emission (ASE) in a low-doped erbium fiber at 976-nm pumping. We demonstrate that ASE noise can be treated as a train of Gaussian-like pulses with random magnitudes, widths, and inter-pulse intervals. ASE noise can also provide a statistical analysis of these three parameters. We also present the data that reveal ASE noise's role in optical spectrum broadening through self-phase modulation of light propagating in a communication fiber. In particular, the data show that the ASE noise derivative defines the broadening's spectral shape.