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We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…

A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…

The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…

In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…

This is the first report on Working Paper WP-RFM-14-01. The potential and capability of sparse representations is well-known. However, their (multivariate variable) vectorial form, which is completely fine in many fields and disciplines,…

This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be…

This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate the instantaneous information of well-separated modes…

In this paper we show that the extraordinary optical transmission phenomenon found before in 2D hole arrays is already present in a linear chain of subwavelength holes, which can be considered as the basic geometrical unit showing this…

In the past ten years, there have been tremendous research progresses on massive MIMO systems, most of which stand from the communications viewpoint. A new trend of investigating massive MIMO, especially for the sparse scenario like…

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…

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…

We present a fully three-dimensional theoretical study of the extraordinary transmission of light through subwavelength hole arrays in optically thick metal films. Good agreement is obtained with experimental data. An analytical minimal…

Resonance diffraction in the periodic array of graphene micro-ribbons is theoretically studied following a recent experiment [L. Ju et al, Nature Nanotech. 6, 630 (2011)]. Systematic studies over a wide range of parameters are presented. It…

A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…

Propagation of two dimensional pulses in electromagnetically induced tranparency media in the case of perpendicular storing and retrieving pulses has been analyzed. It has been shown that propagation control of the pulses in optically thick…

This brief note aims at condensing some results on the 32-point approximate DFT and discussing its arithmetic complexity.

This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…

Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…

We report the most recent progress in understanding the emission properties of millisecond pulsars.