  The statistics of signal increments are commonly used in order to test for
possible 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 classical
phenomenological relationship between the scaling exponents of the second-order
structure function and of the power spectrum does not hold. We show that in
these conditions the relevant quantities to compute are the second or higher
degree differences of the signal. Using this statistical framework to analyze a
synthetic signal and experimental data of wave turbulence on a fluid surface,
we accurately characterize intermittency of these data with steep power
spectra. The general application of this methodology to study intermittency of
experimental signals with steep power spectra is discussed.
