Applied and Numerical Harmonic Analysis
Volume 68 / 2015
Page
%P
-
Book Series
-
Chapter
Post-Fourier Frequencies: Variations and Paradoxes
We address two questions related to the notion of frequency and its possible extensions in the case of evolutive situations, some of them leading to paradoxes. We first make a distinction between the concepts ...
-
Book
-
Article
A new clustering method to explore the dynamics of research communities
Description of temporal networks and detection of dynamic communities have been hot topics of research for the last decade. However, no consensual answers to these challenges have been found due to the complex...
-
Chapter
Transformation from Graphs to Signals and Back
Network science has been a rapidly evolving field to study systems made of interactions between entities. Studying the structure of such networks reveals indeed the underlying mechanisms of these systems, and ...
-
Article
A Note on Reassigned Gabor Spectrograms of Hermite Functions
An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limi...
-
Chapter
A Dynamical Network View of Lyon’s Vélo’v Shared Bicycle System
Community shared bicycle systems are an instance of public transportation systems that provide digital footprints of all the movements made using this system. The completeness of such dataset allows for their ...
-
Article
Open AccessRecent Advances in Theory and Methods for Nonstationary Signal Analysis
-
Chapter
Time-Frequency/Time-Scale Reassignment
This chapter reviews the reassignment principle, which aims at “sharpening” time-frequency and time-scale representations in order to improve their readability.
-
Chapter
From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation
The Lamperti transformation defines a one-to-one correspondence between stationary processes on the real line and self-similar processes on the real half-line. Although dating back to 1962, this fundamental re...
-
Chapter and Conference Paper
Reassigned Scalograms and Singularities
Reassignment is a general nonlinear technique aimed at increasing the localization of time-frequency and time-scale distributions. Its principle consists in supplementing an energy distribution with a suitable...
-
Chapter
Inequalities in Mellin-Fourier Signal Analysis
A specific form of the Mellin transform, referred to as the “scale transform,” is known to be a natural complement to the Fourier transform for wide-band analytic signals. In this chapter, limitations for the ...
-
Chapter and Conference Paper
Wavelets for Scaling Processes
Depending on the considered range of scales, different scaling processes may be defined, which correspond to different situations connected with self-similarity, fractality or long-range dependence. Wavelet analy...
-
Article
On the Statistics of Spectrogram Reassignment Vectors
Reassignment is a non-linear technique which can improve on the localization of a spectrogram by moving its values according to a suitable vector field. Statistical properties of spectrogram reassignment vecto...
-
Chapter
On the Statistics of Spectrogram Reassignment Vectors
Reassignment is a non-linear technique which can improve on the localization of a spectrogram by moving its values according to a suitable vector field. Statistical properties of spectrogram reassignment vecto...
-
Chapter
Wavelets, spectrum analysis and 1/f processes
The purpose of this paper is to evidence why wavelet-based estimators are naturally matched to the spectrum analysis of 1/f processes. It is shown how the revisiting of classical spectral estimators from a time-f...
-
Chapter
Time-scale analyses and self-similar stochastic processes
A number of different physical situations (e.g.,“1 /f noise,” turbulence, texture analysis,… ) give rise to fractal or fractal-like signals, modeled as samples of self-similar processes. This motivates the dev...
-
Chapter
Quelques methodes temps-frequence et temps-echelle en traitement du signal
-
Chapter and Conference Paper
Non-Destructive Evaluation in the Time-Frequency Domain by Means of the Wigner-Ville Distribution
In a number of NDE problems, parameters of interest are related to both temporal and spectral signal descriptions. It is then proposed to introduce mixed tools which consider time and frequency simultaneously....
-
Chapter
Time-Frequency Processing of Bat Sonar Signals
It is known that time-frequency distributions can be used for the demodulation of bat sonar signals and, in some cases, for detection-estimation tasks via a 2-D correlation process. In this paper, we formalize...
