Related papers: An Algorithm for the Continuous Morlet Wavelet Tra…

Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…

In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…

Intrinsic spectrum that results from the coupling of spontaneous emission in a laser cavity, can determine the energy concentration and coherence of lasers, which is crucial for the optical high-precision measurement. Up to now, it is hard…

Using wavelet analysis approach, we can derive a measure of the disorder content of solar activity, following the temporal evolution of the so-called wavelet entropy. The interesting feature of this parameter is its ability to extract a…

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…

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…

For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative…

An imaging refractrometer can be used to describe the properties of a high-energy density plasma by analyzing the transverse intensity distribution of a laser beam that has passed through the plasma. The output of the refractrometer can be…

Morlet or Gabor wavelet transforms as well as Gaussian smoothing, are widely used in signal processing and image processing. However, the computational complexity of their direct calculations is proportional not only to the number of data…

Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…

Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…

Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, formation and dissipation of thin current sheets, stochastic heating. It is now…

The wavelet transform has been used for numerous studies in astrophysics, including signal--noise periodicity and decomposition as well as the signature of differential rotation in stellar light curves. In the present work, we apply the…

Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…

Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…

There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the…

The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…

Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…