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

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

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

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

Statistical Properties of Fluctuations: A Method to Check Market Behavior

We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal behavior of the returns using a recently developed wavelet based fluctuation analysis method. the returns show a fat-tail distribution as also weak non-statistical behavior. We have also carried out continuous wavelet as well as Fourier power spectral analysis to characterize the periodic nature and correlation properties of the time series.Comment: 9 pages, 6 figures, Econophys-IV, Kolkata, 200

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

Novel approach to analysing large data sets of personal sun exposure measurements

Personal sun exposure measurements provide important information to guide the development of sun awareness and disease prevention campaigns. We assess the scaling properties of personal ultraviolet radiation (pUVR) sun exposure measurements using the wavelet transform (WT) spectral analysis to process long-range, high-frequency personal recordings collected by electronic UVR dosimeters designed to measure erythemal UVR exposure. We analysed the sun exposure recordings of school children, farmers, marathon runners and outdoor workers in South Africa, and construction workers and work site supervisors in New Zealand. We found scaling behaviour in all the analysed pUVR data sets. We found that the observed scaling changes from uncorrelated to long-range correlated with increasing duration of sun exposure. Peaks in the WT spectra that we found suggest the existence of characteristic times in sun exposure behaviour that were to some extent universal across our data set. Our study also showed that WT measures enable group classification, as well as distinction between individual UVR exposures, otherwise unattainable by conventional statistical methods