TFAW: wavelet-based signal reconstruction to reduce photometric noise in time-domain surveys

There have been many efforts to correct systematic effects in astronomical light curves to improve the detection and characterization of planetary transits and astrophysical variability. Algorithms like the Trend Filtering Algorithm (TFA) use simultaneously-observed stars to remove systematic effects, and binning is used to reduce high-frequency random noise. We present TFAW, a wavelet-based modified version of TFA. TFAW aims to increase the periodic signal detection and to return a detrended and denoised signal without modifying its intrinsic characteristics. We modify TFA's frequency analysis step adding a Stationary Wavelet Transform filter to perform an initial noise and outlier removal and increase the detection of variable signals. A wavelet filter is added to TFA's signal reconstruction to perform an adaptive characterization of the noise- and trend-free signal and the noise contribution at each iteration while preserving astrophysical signals. We carried out tests over simulated sinusoidal and transit-like signals to assess the effectiveness of the method and applied TFAW to real light curves from TFRM. We also studied TFAW's application to simulated multiperiodic signals, improving their characterization. TFAW improves the signal detection rate by increasing the signal detection efficiency (SDE) up to a factor ~2.5x for low SNR light curves. For simulated transits, the transit detection rate improves by a factor ~2-5x in the low-SNR regime compared to TFA. TFAW signal approximation performs up to a factor ~2x better than bin averaging for planetary transits. The standard deviations of simulated and real TFAW light curves are ~40x better than TFA. TFAW yields better MCMC posterior distributions and returns lower uncertainties, less biased transit parameters and narrower (~10x) credibility intervals for simulated transits. We present a newly-discovered variable star from TFRM.Comment: Accepted for publication by A&A. 13 pages, 16 figures and 5 table

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Analysis and application of digital spectral warping in analog and mixed-signal testing

Spectral warping is a digital signal processing transform which shifts the frequencies contained within a signal along the frequency axis. The Fourier transform coefficients of a warped signal correspond to frequency-domain 'samples' of the original signal which are unevenly spaced along the frequency axis. This property allows the technique to be efficiently used for DSP-based analog and mixed-signal testing. The analysis and application of spectral warping for test signal generation, response analysis, filter design, frequency response evaluation, etc. are discussed in this paper along with examples of the software and hardware implementation

Demodulation of Spatial Carrier Images: Performance Analysis of Several Algorithms Using a Single Image

http://link.springer.com/article/10.1007%2Fs11340-013-9741-6#Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons, especially a lack of metrological performance assessment. A full-field measurement can be characterized by its resolution, bias, measuring range, and by a specific quantity, the spatial resolution. The present paper proposes an original procedure to estimate in one single step the resolution, bias and spatial resolution for a given operator (decoding algorithms such as image correlation, low-pass filters, derivation tools ...). This procedure is based on the construction of a particular multi-frequential field, and a Bode diagram representation of the results. This analysis is applied to various phase demodulating algorithms suited to estimate in-plane displacements.GDR CNRS 2519 “Mesures de Champs et Identification en Mécanique des Solide

Entropic lattice Boltzmann methods

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier-Motzkin elimination, provides an important tool for visualizing the state space of lattice Boltzmann algorithms that conserve a given set of moments of the distribution function. We show how such models can be endowed with a Lyapunov functional, analogous to Boltzmann's H, resulting in unconditional numerical stability. Using the Chapman-Enskog analysis and numerical simulation, we demonstrate that such entropically stabilized lattice Boltzmann algorithms, while fully explicit and perfectly conservative, may achieve remarkably low values for transport coefficients, such as viscosity. Indeed, the lowest such attainable values are limited only by considerations of accuracy, rather than stability. The method thus holds promise for high-Reynolds number simulations of the Navier-Stokes equations.Comment: 54 pages, 16 figures. Proc. R. Soc. London A (in press