Data reduction methods for single-mode optical interferometry - Application to the VLTI two-telescopes beam combiner VINCI

The interferometric data processing methods that we describe in this paper use a number of innovative techniques. In particular, the implementation of the wavelet transform allows us to obtain a good immunity of the fringe processing to false detections and large amplitude perturbations by the atmospheric piston effect, through a careful, automated selection of the interferograms. To demonstrate the data reduction procedure, we describe the processing and calibration of a sample of stellar data from the VINCI beam combiner. Starting from the raw data, we derive the angular diameter of the dwarf star Alpha Cen A. Although these methods have been developed specifically for VINCI, they are easily applicable to other single-mode beam combiners, and to spectrally dispersed fringes.Comment: Accepted for publication in Astronomy & Astrophysics, 17 pages, 19 figure

Enhanced Wavelet Analysis of Solar Magnetic Activity with Comparison to Global Temperature and the Central England Temperature Record

The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.Comment: 19 pages, 11 figure

Wavelet Based Fractal Analysis of Airborne Pollen

The most abundant biological particles in the atmosphere are pollen grains and spores. Self protection of pollen allergy is possible through the information of future pollen contents in the air. In spite of the importance of airborne pol len concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of the daily pollen forecasts have resulted in failures. Previous analysis of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply the wavelet transform to study the multifractal characteristics of an a irborne pollen time series. We find the persistence behaviour associated to low pollen concentration values and to the most rare events of highest pollen co ncentration values. The information and the correlation dimensions correspond to a chaotic system showing loss of information with time evolution.Comment: 11 pages, 7 figure

Instantaneous frequency and amplitude identification using wavelets: Application to glass structure

This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification to the well-known Morlet wavelet to allow analysis at high resolution. In order to interpret the CWT of a signal correctly, an approximate analytic expression for the CWT of an oscillatory signal is examined via a stationary-phase approximation. This analysis is specialized for the new wavelet and the results are used to construct expressions for the amplitude and frequency modulations of the components in a signal from the transform of the signal. The method is tested on a representative, variable-frequency signal as an example before being applied to a function of interest in our subject area - a structural correlation function of a disordered material - which immediately reveals previously undetected features.Comment: 9 pages, 19 figures; v1.04 higher quality diagrams, removed mathematica font requirement

Quantum tomography with wavelet transform in Banach space on Homogeneous space

The intimate connection between the Banach space wavelet reconstruction method on homogeneous spaces with both singular and nonsingular vacuum vectors, and some of well known quantum tomographies, such as: Moyal-representation for a spin, discrete phase space tomography, tomography of a free particle, Homodyne tomography, phase space tomography and SU(1,1) tomography is explained. Also both the atomic decomposition and banach frame nature of these quantum tomographic examples is explained in details. Finally the connection between the wavelet formalism on Banach space and Q-function is discussed.Comment: 25 page

Solar-like oscillations with low amplitude in the CoRoT target HD 181906

Context: The F8 star HD 181906 (effective temperature ~6300K) was observed for 156 days by the CoRoT satellite during the first long run in the centre direction. Analysis of the data reveals a spectrum of solar-like acoustic oscillations. However, the faintness of the target (m_v=7.65) means the signal-to-noise (S/N) in the acoustic modes is quite low, and this low S/N leads to complications in the analysis. Aims: To extract global variables of the star as well as key parameters of the p modes observed in the power spectrum of the lightcurve. Methods: The power spectrum of the lightcurve, a wavelet transform and spot fitting have been used to obtain the average rotation rate of the star and its inclination angle. Then, the autocorrelation of the power spectrum and the power spectrum of the power spectrum were used to properly determine the large separation. Finally, estimations of the mode parameters have been done by maximizing the likelihood of a global fit, where several modes were fit simultaneously. Results: We have been able to infer the mean surface rotation rate of the star (~4 microHz) with indications of the presence of surface differential rotation, the large separation of the p modes (~87 microHz), and therefore also the ridges corresponding to overtones of the acoustic modes.Comment: Paper Accepted to be published in A&A. 10 Pages, 12 figure

Multiscale analysis of waves reflected by complex interfaces: Basic principles and experiments

International audience[1] This paper considers the reflection of waves by multiscale interfaces in the framework of the wavelet transform. First, we show how the wavelet transform is efficient to detect and characterize abrupt changes present in a signal. Locally homogeneous abrupt changes have conspicuous cone-like signatures in the wavelet transform from which their regularity may be obtained. Multiscale clusters of nearby singularities produce a hierarchical arrangement of conical patterns where the multiscale structure of the cluster may be identified. Second, the wavelet response is introduced as a natural extension of the wavelet transform when the signal to be analyzed (i.e., the velocity structure of the medium) can only be remotely probed by propagating wavelets into the medium instead of being directly convolved as in the wavelet transform. The reflected waves produced by the incident wavelets onto the reflectors present in the medium constitute the wavelet response. We show that both transforms are equivalent when multiple scattering is neglected and that cone-like features and ridge functions can be recognized in the wavelet response as well. Experimental applications of the acoustical wavelet response show how useful information can be obtained about remote multiscale reflectors. A first experiment implements the synthetic cases discussed before and concerns the characterization of planar reflectors with finite thicknesses. Another experiment concerns the multiscale characterization of a complex interface constituted by the surface of a layer of monodisperse glass beads immersed in water. Citation: Le Gonidec, Y., D. Gibert, and J.-N. Proust , Multiscale analysis of waves reflected by complex interfaces: Basic principles and experiments

A Methodology for Detecting Field Potentials from the External Ear Canal: NEER and EVestG

An algorithm called the neural event extraction routine (NEER) and a method called Electrovestibulography (EVestG) for extracting field potentials (FPs) from artefact rich and noisy ear canal recordings is presented. Averaged FP waveforms can be used to aid detection of acoustic and or vestibular pathologies. FPs were recorded in the external ear canal proximal to the ear drum. These FPs were extracted using an algorithm called NEER. NEER utilises a modified complex Morlet wavelet analysis of phase change across multiple scales and a template matching (matched filter) methodology to detect FPs buried in noise and biological and environmental artefacts. Initial simulation with simulated FPs shows NEER detects FPs down to −30 dB SNR (power) but only 13–23% of those at SNR’s <−6 dB. This was deemed applicable to longer duration recordings wherein averaging could be applied as many FPs are present. NEER was applied to detect both spontaneous and whole body tilt evoked FPs. By subtracting the averaged tilt FP response from the averaged spontaneous FP response it is believed this difference is more representative of the vestibular response. Significant difference (p < 0.05) between up and down whole body (supine and sitting) movements was achieved. Pathologic and physiologic evidence in support of a vestibular and acoustic origin is also presented

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition