This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions which are eigenfunctions of the continuous Fourier transform and by performing a novel error removal procedure. Then, the result of the eigendecomposition of the DFT matrix...

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof depends on an extrapol...

The standard method for spectrum analysis in digital signal processing (DSP) is the discrete Fourier transform (DFT), typically implemented using a fast Fourier transform (FFT) algorithm. However, there are applications that require spectrum analysis only over a subset of the N center frequencies of an N-point DFT. A popular, as well as efficient, technique for computing sparse DFT results is t...

Discrete Fourier Transform (DFT) is probably the most popular signal processing tool. Wide DFT use is partly dedicated to fast Fourier Transform (FFT) algorithms (Cooley & Tukey, 1965, Oppenheim et al., 1999, Lyons, 2004). DFT may also be efficiently computed by recursive algorithms in the window sliding by one sample (Jacobsen & Lyons, 2003, Duda, 2010). Unfortunately, DFT has two main drawbac...

Electronic structure calculations are now indispensible for understanding chemical phenomena. Density functional theory (DFT), which is simple, conceptual, and applicable to large systems, has emerged as a powerful computational tool to tackle molecular electronic structures. DFT efficiently calculates electronic structure with high accuracy, and its algorithm is suitable for parallel computing...

BACKGROUND An increased defibrillation threshold (DFT) may limit the efficacy of an implantable cardioverter-defibrillator (ICD) in termination of life-threatening ventricular arrhythmias. A search for methods of decreasing DFT has been ongoing since the introduction of ICD into clinical practice. AIM To assess the effects of various shock polarities on DFT. METHODS The study group consiste...

Periodic density functional theory (DFT) calculations have recently emerged as a popular tool for assigning solid-state nuclear magnetic resonance (NMR) spectra. However, in order for the calculations to yield accurate results, accurate structural models are also required. In many cases the structural model (often derived from crystallographic diffraction) must be optimised (i.e., to an energy ...