Testing for high frequency features in a noisy signal.

Summary The aim of this article is to detect high frequency (HF) features in a noisy signal. We propose a parametric characterization in the Fourier domain of the HF features. Then we introduce a procedure to evaluate these parameters and compute a p-value which assesses in a quantitative manner the presence or absence of such features, that we also call "oscillations". The procedure is well adapted for real 1-dimensional signals. If the signal analyzed has singular events in the low frequencies, the first step is a data-driven regularization of its Fourier transform. In the second step, the HF features parameters are estimated. The third step is the computation of the p-value thanks to a Monte Carlo procedure. The test is conducted on sanity-check signals where the ratio amplitude of the oscillations/level of the noise is entirely controlled. The test detects HF features even when the level of the noise is five times larger than the amplitude of the oscillations. The test is also conducted on signals from Prion disease experiments and confirms the presence of HF features in these signals.