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A theoretical and experimental analysis of the pump-noise contribution to frequency noise and linewidth in distributed-feedback fiber lasers is presented. An analytic expression for the frequency domain transfer function from pump to frequency fluctuations is derived and a formula for the pump-dependent frequency noise spectrum given. These results are confirmed experimentally for two dissimilar distributed-feedback fiber lasers with moderate Er concentration. The transition from fundamental thermal noise at low pump intensity to pump induced frequency noise at high pump intensity is experimentally observed, thus, clarifying the general nature of frequency noise in compact fiber lasers. The relationship between frequency noise and linewidth is discussed.