We present a frequency domain solution to the sampled-data passivity problem. Our analysis is exact in the sense that we take into account the intersample behavior of the system. We use frequency response (FR) operators to first obtain necessary conditions on the sampling rate T and the relative degree of the open-loop transfer function G11 for achieving a passive continuous-time closed-loop system. Then, assuming passivity of G11 and closed-loop stability, we derive a necessary and sufficient condition for discrete-time controllers that render a passive closed-loop system. We apply the obtained results to the problem of stability of haptic systems.