A real-time spectral analysis is demonstrated experimentally with a frequency-shifting loop that includes an electro-optic phase modulator. When a single-frequency laser seeds the loop, pulse doublets are emitted if the integer Talbot condition is satisfied. With a polychromatic seed, frequency-to-time mapping is demonstrated, namely the temporal output of the loop maps the spectral power of the seed, with a resolution of 400 kHz. Due to the phase modulation function, the mapping is shown to be nonlinear. The results are in agreement with the theoretical predictions of [H. Yang et al., J. Opt. Soc. Am. B37, 3162 (2020)JOBPDE0740-322410.1364/JOSAB.389801]. The extension to integrated systems for applications is discussed.