Related papers: An Algorithm for the Continuous Morlet Wavelet Tra…
The traditional continuous wavelet transform is plagued by the cone-of-influence, ie wavelets which extend past either end of a finite timeseries return transform coefficients which tend to decrease as more of the wavelet is truncated.…
The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the…
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…
A short, abrupt increase in energy injection rate into steady strongly-driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized in time and space and its spectra differ…
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of…
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…
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…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
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…
We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Using a continuous wavelet transform we have analyzed the cycle-to-cycle variations of pressure in an internal combustion engine. The time series of maximum pressure variations are examined for different loading and their wavelet power…
The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial…
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…
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the…
In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…
Many continuous wavelets are defined in the frequency domain and do not have analytical expressions in the time domain. Meyer wavelet is ordinarily defined in this way. In this note, we derive new straightforward analytical expressions for…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…