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A fast-wave pulse in a simple, cold, inhomogeneous MHD model plasma is constructed by Fourier superposition over frequency of harmonic waves that are singular at their respective Alfven resonances. The pulse partially reflects before…
We numerically analyse extraordinary terahertz transmission properties of an array of rectangular shaped apertures perforated periodically on a thin metal film. The apertures are tapered at different angles to achieve higher field…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…
Plasmons in low-dimensional systems respresent an important tool for coupling energy into nanostructures and the localization of energy on the scale of only a few nanometers. Contrary to ordinary surface plasmons of metallic bulk materials,…
Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a…
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution…
Recently, style transfer is a research area that attracts a lot of attention, which transfers the style of an image onto a content target. Extensive research on style transfer has aimed at speeding up processing or generating high-quality…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
Light transport in a metal with two-dimensional hole arrays is considered. Analytical expression for a transmission coefficient in periodic, isolated and disordered cases are derived, assuming the existence of waveguide modes transverse…
Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nano-sized objects with a single x-ray laser shot. The enormous data sets with up to several million…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.
We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…
This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing…