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Testing for high frequency features in a noisy signal

Mezache, Mathieu; Hoffmann, Marc; Rezaei, Human; Doumic, Marie (2019-08), Testing for high frequency features in a noisy signal. https://basepub.dauphine.fr/handle/123456789/20179

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02263522
Date
2019-08
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
28
Metadata
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Author(s)
Mezache, Mathieu
Laboratoire Jacques-Louis Lions [LJLL]
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rezaei, Human
Unité de recherche Virologie et Immunologie Moléculaires [VIM (UR 0892)]
Doumic, Marie
Laboratoire Jacques-Louis Lions [LJLL]
Abstract (EN)
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.
Subjects / Keywords
Spectral analysis; Monte Carlo methods; Hypothesis testing; Prions; Signal detection and filtering; Static Light Scattering; Discrete Fourier transform

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