Abstract Coherent microwave-to-optical conversion is crucial for transferring quantum information generated in the microwave domain to optical frequencies, where propagation losses can be minimized. Coherent, atom-based transducers have shown rapid progress in recent years. This paper reports an experimental demonstration of coherent microwave-to-optical conversion that maps a microwave signal to a large, tunable 550(30) MHz range of optical frequencies using room-temperature 87Rb atoms. The inhomogeneous Doppler broadening of the atomic vapor advantageously supports the tunability of an input microwave channel to any optical frequency channel within the Doppler width, along with the simultaneous conversion of a multi-channel input microwave field to corresponding optical channels. In addition, we demonstrate phase-correlated amplitude control of select channels, providing an analog to a frequency domain beam splitter across five orders of magnitude in frequency. With these capabilities, neutral atomic systems may also be effective quantum processors for quantum information encoded in frequency-bin qubits.