We experimentally show that the response of a quantum-chaotic system can display resonance lines sharper than the inverse of the excitation duration. This allows us to discriminate two neighboring frequencies with a resolution nearly 40 times better than the limit set by the Fourier inequality. Furthermore, numerical studies indicate that there is no limit, but the loss of signal, to this resolution, opening ways for the development of sub-Fourier quantum-chaotic signal processing.
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