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This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…

Statistics Theory · Mathematics 2008-03-27 Jean-Marc Bardet , Hatem Bibi , Abdellatif Jouini

Temporal and spectral information extracted from a stream of photons received from astronomical sources is the foundation on which we build understanding of various objects and processes in the Universe. Typically astronomers fit a number…

High Energy Astrophysical Phenomena · Physics 2016-11-18 T. N. Ukwatta , P. R. Wozniak

Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of…

Statistics Theory · Mathematics 2018-11-27 Sophie Achard , Irène Gannaz

Feature extraction for automatic classification of EEG signals typically relies on time frequency representations of the signal. Techniques such as cepstral-based filter banks or wavelets are popular analysis techniques in many signal…

Signal Processing · Electrical Eng. & Systems 2018-01-09 Amir Harati , Meysam Golmohammadi , Silvia Lopez , Iyad Obeid , Joseph Picone

In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first…

Fluid Dynamics · Physics 2011-07-20 Y. X. Huang , F. G. Schmitt , J. -P. Hermand , Y. Gagne , Z. M. Lu , Y. L. Liu

Numerous metrics of heart rate variability (HRV) have been described, analyzed, and compared in the literature. However, they rarely cover the actual metrics used in a class of HRV data acquisition devices - those designed primarily to…

Quantitative Methods · Quantitative Biology 2013-08-30 Clinton F. Goss , Eric B. Miller

A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…

Data Analysis, Statistics and Probability · Physics 2008-12-02 Dilip P. Ahalpara , Amit Verma , Prasanta K. Panigrahi , Jitendra C. Parikh

Hurst exponent is an important feature summarizing the noisy high-frequency data when the inherent scaling pattern cannot be described by standard statistical models. In this paper, we study the robust estimation of Hurst exponent based on…

Methodology · Statistics 2017-09-27 Chen Feng , Brani Vidakovic

This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via…

Signal Processing · Electrical Eng. & Systems 2025-12-16 Indrakshi Dey , Ilias Cherkaoui , Mohamed Khalafalla Hassan

We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key…

Signal Processing · Electrical Eng. & Systems 2022-11-28 Wolfgang Erb

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…

Signal Processing · Electrical Eng. & Systems 2023-06-28 Ka Man Yim , Jacob Leygonie

The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…

General Relativity and Quantum Cosmology · Physics 2024-05-27 Andrea Virtuoso , Edoardo Milotti

Power measurement algorithms based on Fourier transform are susceptible to errors caused by interharmonics, while wavelet transform algorithms are particularly sensitive to even harmonics due to band decomposition effects. The empirical…

Signal Processing · Electrical Eng. & Systems 2025-02-17 Jian Liu , Wei Zhao , Shisong Li

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

Classical Analysis and ODEs · Mathematics 2017-03-07 Stefan Lafon , Jacques Lévy Véhel , Jacques Peyrière

Non-cooperative communications using non-orthogonal multicarrier signals are challenging since self-created inter carrier interference (ICI) exists, which would prevent successful signal classification. Deep learning (DL) can deal with the…

Signal Processing · Electrical Eng. & Systems 2020-06-23 Tongyang Xu , Izzat Darwazeh

Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the…

Computer Vision and Pattern Recognition · Computer Science 2024-10-28 Yuan Huang , Valentin De Bortoli , Fugen Zhou , Jerome Gilles

Heart Rate Variability (HRV) plays an important role for reporting several cardiological and non-cardiological diseases. Also, the HRV has a prognostic value and is therefore quite important in modelling the cardiac risk. The nature of the…

Systems and Control · Computer Science 2015-08-06 Mazhar B. Tayel , Eslam I AlSaba

Automatic heart sound abnormality detection can play a vital role in the early diagnosis of heart diseases, particularly in low-resource settings. The state-of-the-art algorithms for this task utilize a set of Finite Impulse Response (FIR)…

Computer Vision and Pattern Recognition · Computer Science 2019-04-25 Ahmed Imtiaz Humayun , Shabnam Ghaffarzadegan , Zhe Feng , Taufiq Hasan

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…

Functional Analysis · Mathematics 2013-11-06 David I Shuman , Christoph Wiesmeyr , Nicki Holighaus , Pierre Vandergheynst

Wavelet transform of polarized fluorescence spectra of human breast tissues is found to localize spectral features that can reliably differentiate normal and malignant tissue types. The intensity differences of parallel and perpendicularly…

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