We report coherent time-to-frequency mapping in frequency shifting loops (FSLs). We show that when seeded by a temporal signal shorter than the inverse of the frequency shift per roundtrip, the optical spectrum at the FSL output consists of a periodic replica of the input waveform, whose temporal amplitude and phase profiles are mapped into the frequency domain. We provide an experimental demonstration of this phenomenon and show how this simple setup enables real-time measurement of fast non-repetitive input RF signals with a detection chain two orders of magnitude slower than the input signal.