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Contributions to the analysis of multicomponent signals : synchrosqueezing and associated methods

Abstract : Many physical signals including audio (music, speech), medical data (ECG, PCG), marine mammals or gravitational-waves can be accurately modeled as a superposition of amplitude and frequency-modulated waves (AM-FM modes), called multicomponent signals (MCSs). Time-frequency (TF) analysis plays a central role in characterizing such signals and in that framework, numerous methods have been proposed over the last decade. However, these methods suffer from an intrinsic limitation known as the uncertainty principle. In this regard, reassignment method (RM) was developed with the purpose of sharpening TF representations (TFRs) given respectively by the short-time Fourier transform (STFT) or the continuous wavelet transform (CWT). Unfortunately, it did not allow for mode reconstruction, in opposition to its recent variant known as synchrosqueezing transforms (SST). Nevertheless, many critical problems associated with the latter still remain to be addressed such as the weak frequency modulation condition, the mode retrieval of an MCS from its downsampled STFT or the TF signature estimation of irregular and discontinuous signals. This dissertation mainly deals with such problems in order to provide more powerful and accurate invertible TF methods for analyzing MCSs.This dissertation gives six valuable contributions. The first one introduces a second-order extension of wavelet-based SST along with a discussion on its theoretical analysis and practical implementation. The second one puts forward a generalization of existing STFT-based synchrosqueezing techniques known as the high-order STFT-based SST (FSSTn) that enables to better handle a wide range of MCSs. The third one proposes a new technique established on the second-order STFT-based SST (FSST2) and demodulation procedure, called demodulation-FSST2-based technique (DSST2), enabling a better performance of mode reconstruction. The fourth contribution is that of a novel approach allowing for the retrieval of modes of an MCS from its downsampled STFT. The fifth one presents an improved method developed in the reassignment framework, called adaptive contour representation computation (ACRC), for an efficient estimation of TF signatures of a larger class of MCSs. The last contribution is that of a joint analysis of ACRC with non-negative matrix factorization (NMF) to enable an effective denoising of phonocardiogram (PCG) signals.
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Duong Hung Pham. Contributions to the analysis of multicomponent signals : synchrosqueezing and associated methods. Signal and Image Processing. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAM044⟩. ⟨tel-01881995v2⟩

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