  Given nonstationary data, one generally wants to extract the trend from the
noise by smoothing or filtering. However, it is often important to delineate a
third intermediate category, that we call high frequency (HF) features: this is
the case in our motivating example, which consists in experimental measurements
of the time-dynamics of depolymerising protein fibrils average size. One may
intuitively visualise HF features as the presence of fast, possibly
nonstationary and transient oscillations, distinct from a slowly-varying trend
envelope. The aim of this article is to propose an empirical definition of HF
features and construct estimators and statistical tests for their presence
accordingly, when the data consists of a noisy nonstationary 1-dimensional
signal. We propose a parametric characterization in the Fourier domain of the
HF features by defining a maximal amplitude and distance to low frequencies of
significant energy. We introduce a data-driven procedure to estimate these
parameters, and compute a p-value proxy based on a statistical test for the
presence of HF features. The test is first conducted on simulated signals where
the ratio amplitude of the HF features to the level of the noise is controlled.
The test detects HF features even when the level of noise is five times larger
than the amplitude of the oscillations. In a second part, the test is conducted
on experimental data from Prion disease experiments and it confirms the
presence of HF features in these signals with significant confidence.
