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The statistics of signal increments are commonly used in order to test forpossible intermittent properties in experimental or synthetic data. However,for signals with steep power spectra [i.e., $E(\omega) \sim \omega^{-n}$ with$n \geq 3$], the increments are poorly informative and the classicalphenomenological relationship between the scaling exponents of the second-orderstructure function and of the power spectrum does not hold. We show that inthese conditions the relevant quantities to compute are the second or higherdegree differences of the signal. Using this statistical framework to analyze asynthetic signal and experimental data of wave turbulence on a fluid surface,we accurately characterize intermittency of these data with steep powerspectra. The general application of this methodology to study intermittency ofexperimental signals with steep power spectra is discussed.

Revealing intermittency in experimental data with steep power spectra