Many existing results on the analysis of OFDM systems are based on an analog representation. The actual implementation of OFDM transmitters typically consists of a discrete DFT matrix and a digital-to-analog (DAC) converter. In this paper, we show that the analog representation admits the implementation of a DFT matrix followed by a DAC converter only in special cases. Necessary and sufficient ...

Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the analog s-d...

With the choice of tungsten as a material for ITER plasma facing components, suprathermal electron interaction with non-fully ionized impurities emerged an important issue in modeling. Microwave heating and current drive systems, especially lower hybrid drive, can generate significant population electrons plasma. Also, case runaway generation mitigation by massive gas injection, collisions have...

A large number of fast Fourier transform (FFT) algorithms exist for efficient computation of the discrete Fourier transform (DFT). In most previous benchmarking efforts, only the computation speed or the operations count have been used for assessing the efficiency of these algorithms. In this paper we provide a comprehensive comparison of several contemporary FFT algorithms on state-of-the-art ...

In this paper, we present an algorithm to estimate a signal from its modified short-time Fourier transform (STFT). This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, we also develop an iterative algorithm to estimate a signal from its modified STFT magnitude. The iter...

The nature of the bonding in model complexes of di-copper metalloenzymes has been analyzed by means of the electronic localization function (ELF) and by the quantum theory of atoms in molecules (QTAIM). The constrained space orbital variations (CSOV) approach has also been used. Density functional theory (DFT) and CASSCF calculations have been carried out on several models of tyrosinase such as...

The rigidity of a matrix M is the function R M (r), which, for a given r, gives the minimum number of entries of M which one has to change in order to reduce its rank to at most r. This notion has been introduced by Valiant in 1977 in connection with the complexity of computing linear forms. Despite more than 20 years of research, very little is known about the rigidity of matrices. Nonlinear l...

This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses few...

We present a composite procedure for the quantum-chemical computation of spin-spin-coupled 1 H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight-binding method GFN-xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the sp...

Recently we have successfully exploited and applied the new and powerful non-parametric Integrated Nested Laplace Approximation (INLA) Bayesian inference method to the problem of Superresolution (SR) image reconstruction, generating the INLA SR algorithm. Even though achieving superior image reconstruction results in comparison to other state-of-the-art methods, such algorithm manipulates matri...