Related papers: Scaling analyses based on wavelet transforms for t…
Precise knowledge of a laser's wavelength is crucial for applications from spectroscopy to telecommunications. Here we present a wavemeter which operates on the Talbot effect. Tone parameter extraction algorithms are used to retrieve the…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
When light is incident upon a diffraction grating, images of the grating appear at periodic intervals behind the grating. This phenomenon and the associated self-imaging distance were named after Talbot who first observed them in the…
We study the multifractal analysis (MFA) of electronic wavefunctions at the localisation-delocalisation transition in the 3D Anderson model for very large system sizes up to $240^3$. The singularity spectrum $f(\alpha)$ is numerically…
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…
We extend the theory of Talbot revivals for planar or rectangular geometry to the case of cylindrical waveguides. We derive a list of conditions that are necessary to obtain revivals in cylindrical waveguides. A phase space approach based…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and…
In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…
This paper presents a method for background removal in experimental data processing using the Dual-Tree Complex Wavelet Transform (DTCWT). The technique is based on discrete wavelet theory (DWT) and addresses limitations of commonly used…
The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an…
We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional…
It has been noticed recently that transverse momenta (p_T) distributions observed in high energy production processes exhibit remarkably universal scaling behaviour. This is the case when a suitable variable replaces the usual p_T. On the…
For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…
Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…
It is shown how wavelets may be used to analyse the absorption properties of the Lya forest. The Discrete Wavelet Transform of a QSO spectrum is used to decompose the light fluctuations that comprise the forest into orthogonal wavelets. It…