We consider a periodically modulated random walk (Wiener process) to an absorbing barrier with a deterministic reset to the starting point following each barrier crossing. Cooperative effects arising from the interplay between the noise and periodic modulation are analyzed as they manifest themselves in two statistical measures of the response: the passage time statistics of the process and the power spectral density of the output. Simple relationships exist between the extrema that occur in these two characterizations. The spectral properties of the response are seen to bear a striking resemblance to the stochastic resonance phenomenon that is known to occur in periodically driven noisy nonlinear systems.PACS number(s): 05.40.+j

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