The spectrum of amplified spontaneous Raman scattering and gain in a fiber Raman amplifer has been calculated analytically as a function of distance and pump power. The model used makes no assumptions on the magnitude of the gain and considers the pump nondepletion region. From the results, the on/off ratio has been calculated and is found to have a variation with length that depends on frequency detuning. An enhancement in on/off ratio is also found for small fiber lengths but at limited gain. The use of a narrow-bandpass optical fiber leads to quite different behavior of the on/off ratio than for the unfiltered case.