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Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…
Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
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.
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
Transformer architectures, underpinned by the self-attention mechanism, have achieved state-of-the-art results across numerous natural language processing (NLP) tasks by effectively modeling long-range dependencies. However, the…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…
We introduce a ScatterNet that uses a parametric log transformation with Dual-Tree complex wavelets to extract translation invariant representations from a multi-resolution image. The parametric transformation aids the OLS pruning algorithm…
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
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…
We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation…
We report on a calculation to show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable \zeta at fixed invariant momentum transfer squared t gives results that are…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Power measurement algorithms based on Fourier transform are susceptible to errors caused by interharmonics, while wavelet transform algorithms are particularly sensitive to even harmonics due to band decomposition effects. The empirical…
Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use…
We investigate some interesting solutions in the DSR theories. These solutions have important features in optics and mechanics. We use these similarities for a better understanding of these theories. We know that, the vacuum in the DSR has…
Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes…
In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…