  We study an aspect of the following general question: which properties of a
signal can be characterized by its scattering transform? We show that the
energy contained in high order scattering coefficients is upper bounded by the
energy contained in the high frequencies of the signal. This result links the
decay of the scattering coefficients of a signal with the decay of its Fourier
transform. Additionally, it allows to generalize some results of Mallat (2012),
by relaxing the admissibility condition on the wavelet family.
