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Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We…
In an earlier paper (Ahuja, et al, 2005), based on simultaneous multi-frequency observations with the Giant Metrewave Radio Telescope (GMRT), we reported the variation of pulsar dispersion measures (DMs) with frequency. A few different…
We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of…
Transposed convolution is crucial for generating high-resolution outputs, yet has received little attention compared to convolution layers. In this work we revisit transposed convolution and introduce a novel layer that allows us to place…
The design, fabrication, and optical properties of a composite plasmonic structure, a two-dimentional array of split-ring resonators inserted into periodic square holes of a metal film, have been reported. A new type of transmission…
Electronic metadevices leveraging sub-wavelength metallic features have shown great potential for high-frequency switching. Theoretical analysis based on a one-dimensional (1D) model indicates that reducing the size of subwavelength…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
We investigate the collective plasmonic modes of metal nano-particles in periodic two-dimensional (2D) arrays within a point-dipole description. As an open system, the full-dynamic dispersion relations of the 2D arrays are obtained through…
This short paper is based on the talk of the second author given at the 2005 Hayama Symposium on Complex Analysis in Several Variables. The recent results of the authors on the spectrum of quantum tubes are summarized.
This report elaborates on approximations for the discrete Fourier transform by means of replacing the exact Cooley-Tukey algorithm twiddle-factors by low-complexity integers, such as $0, \pm \frac{1}{2}, \pm 1$.
The basic form of drifting sub-pulses is that of a periodicity whose phase depends (approximately linearly) on both pulse longitude and pulse number. As such, we argue that the two-dimensional Fourier transform of the longitude-time data…
This letter is to introduce delay Doppler transform (DDT) for a time domain signal. It is motivated by the recent studies in wireless communications over delay Doppler channels that have both time and Doppler spreads, such as, satellite…
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…
We have proposed and developed a method to utilize attosecond pulses in diffraction imaging techniques applied to complex samples. In this study, the effects of the broadband properties of the wavefield owing to attosecond pulses are…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium,…
Subradiance is a phenomenon where coupled emitters radiate light at a slower rate than independent ones. While its observation was first reported in disordered cold atom clouds, ordered subwavelength arrays of emitters have emerged as…