The application of a Trous wave filtering and Monte Carlo analysis on SECIS 2001 solar eclipse observations

8000 images of the Solar corona were captured during the June 2001 total Solar eclipse. New software for the alignment of the images and an automated technique for detecting intensity oscillations using multi scale wavelet analysis were developed. Large areas of the images covered by the Moon and the upper corona were scanned for oscillations and the statistical properties of the atmospheric effects were determined. The a Trous wavelet transform was used for noise reduction and Monte Carlo analysis as a significance test of the detections. The effectiveness of those techniques is discussed in detail.Comment: 17 pages, 8 figures, accepted by Solar Physics Journal for publication in Topical Issue: "Frontiers in Solar Image Processing

Introduction to the Analysis of Low-Frequency Gravitational Wave Data

The space-based gravitational wave detector LISA will observe in the low-frequency gravitational-wave band (0.1 mHz up to 1 Hz). LISA will search for a variety of expected signals, and when it detects a signal it will have to determine a number of parameters, such as the location of the source on the sky and the signal's polarisation. This requires pattern-matching, called matched filtering, which uses the best available theoretical predictions about the characteristics of waveforms. All the estimates of the sensitivity of LISA to various sources assume that the data analysis is done in the optimum way. Because these techniques are unfamiliar to many young physicists, I use the first part of this lecture to give a very basic introduction to time-series data analysis, including matched filtering. The second part of the lecture applies these techniques to LISA, showing how estimates of LISA's sensitivity can be made, and briefly commenting on aspects of the signal-analysis problem that are special to LISA.Comment: 20 page

TRUFAS, a wavelet based algorithm for the rapid detection of planetary transits

Aims: We describe a fast, robust and automatic detection algorithm, TRUFAS, and apply it to data that are being expected from the CoRoT mission. Methods: The procedure proposed for the detection of planetary transits in light curves works in two steps: 1) a continuous wavelet transformation of the detrended light curve with posterior selection of the optimum scale for transit detection, and 2) a period search in that selected wavelet transformation. The detrending of the light curves are based on Fourier filtering or a discrete wavelet transformation. TRUFAS requires the presence of at least 3 transit events in the data. Results: The proposed algorithm is shown to identify reliably and quickly the transits that had been included in a standard set of 999 light curves that simulate CoRoT data. Variations in the pre-processing of the light curves and in the selection of the scale of the wavelet transform have only little effect on TRUFAS' results. Conclusions: TRUFAS is a robust and quick transit detection algorithm, especially well suited for the analysis of very large volumes of data from space or ground-based experiments, with long enough durations for the target-planets to produce multiple transit events.Comment: 9 pages, 10 figures, accepted by A&

On wavenumber spectra for sound within subsonic jets

This paper clarifies the nature of sound spectra within subsonic jets. Three problems, of increasing complexity, are presented. Firstly, a point source is placed in a two-dimensional plug flow and the sound field is obtained analytically. Secondly, a point source is embedded in a diverging axisymmetric jet and the sound field is obtained by solving the linearised Euler equations. Finally, an analysis of the acoustic waves propagating through a turbulent jet obtained by direct numerical simulation is presented. In each problem, the pressure or density field are analysed in the frequency-wavenumber domain. It is found that acoustic waves can be classified into three main frequency-dependent groups. A physical justification is provided for this classification. The main conclusion is that, at low Strouhal numbers, acoustic waves satisfy the d'Alembertian dispersion relation.Comment: 20 pages, 9 figure

Discrete Signal Processing on Graphs: Frequency Analysis

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high-, and band-pass graph filters. In traditional signal processing, there concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification

Fast Spectral Variability from Cygnus X-1

We have developed an algorithm that, starting from the observed properties of the X-ray spectrum and fast variability of an X-ray binary allows the production of synthetic data reproducing observables such as power density spectra and time lags, as well as their energy dependence. This allows to reconstruct the variability of parameters of the energy spectrum and to reduce substantially the effects of Poisson noise, allowing to study fast spectral variations. We have applied the algorithm to Rossi X-ray Timing Explorer data of the black-hole binary Cygnus X-1, fitting the energy spectrum with a simplified power law model. We recovered the distribution of the power law spectral indices on time-scales as low as 62 ms as being limited between 1.6 and 1.8. The index is positively correlated with the flux even on such time-scales.Comment: 14 pages, 19 figures, accepted by MNRA