Related papers: Wavelets: mathematics and applications
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
In this short report it is argued that by the use of wavelets formalism it is possible to describe the q-bit state. The wavelet formalism address the real-valued physical signals, for example, obtained during typical physical measurements.
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
The reassignment method for the wavelet transform is investigated. Particularly good results are obtained if the wavelet is an extremal for the uncertainty relation of the affine group.
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…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp…
Aims. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…