New algorithms for computing the Discrete Fourier Transform (DFT) spectra along different directions are derived and implemented. For computing the DFT spectrum along any given direction (containing N DFT frequencies), a new algorithm is presented that requires N ( N 1 ) additions and a single 1-D FFT. As expected, for a single direction, the directional FFT algorithm is significantly faster th...

Recently, we introduced a new density-functional theory ~DFT! approach for the calculation of NMR shielding constants. First, a hybrid DFT calculation ~using 5% exact exchange! is performed on the molecule to determine Kohn–Sham orbitals and their energies; second, the constants are determined as in nonhybrid DFT theory, that is, the paramagnetic contribution to the constants is calculated from...

This paper presents a new fast Discrete Fourier Transform (DFT) algorithm. By rewriting the DFT, a new algorithm is obtained that uses 2 n?2 (3n?13)+4n?2 real multiplications and 2 n?2 (7n? 29) + 6n + 2 real additions for a real data N = 2 n point DFT, comparable to the number of operations in the Split-Radix method, but with slightly fewer multiply and add operations in total. Because of the o...

We discuss the basic concepts of density functional theory (DFT) as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT cons...

In this paper we consider optimal estimators for speech enhancement in the Discrete Fourier Transform (DFT) domain. We derive an analytical solution for estimating complex DFT coefficients in the MMSE sense when the clean speech DFT coefficients are Laplacian distributed and the DFT coefficients of the noise are Gaussian or Laplacian distributed. We show that these estimators have a number of i...

The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. In particular, by clever grouping and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation required). Many “fast” algorithms have been ...

The optical computing technology ooers new challenges to the algorithm designers since it can perform an n-point DFT computation in only unit time. Note that DFT is a non-trivial computation in the PRAM model. We develop two new models, DFT-VLSIO and DFT-Circuit, to capture this characteristic of optical computing. We also provide two paradigms for developing parallel algorithms in these models...

The DFT based OFDM (DFT-OFDM) has currently drawn most of attention in the area of wireless communication. But, there is a long way to go to pursue higher bandwidth efficiency. Discrete wavelet transform has been proposed to substitute DFT, due to its higher spectral containment between subchannels, which can eliminate cyclic prefix (CP) that a must in DFT-OFDM system. In this paper, we propose...

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restr...