We present a framework for algorithm selection, code generation and optimization for the Fast Fourier Transform. The framework consists of two main parts – the DFT Code Generator (FftGen) and the Execution Scheduler (FftPlanner). The library generator outputs a highly optimized set of small to modest size DFT codelets written in ‘C’. The FftPlanner searches an exponential space of possible algo...

A DFT algorithm, the Extended Subband DFT (ESB−−DFT), is presented, which aims to overcome the problem of low accuracy the Subband DFT (SB−−DFT) algorithm suffers from, when applied in its approximate mode for signals with full spectrum. The proposed ESB−DFT is based upon the analysis of the input signal using a Filter Bank (FB) and the computation of its DFT from the lower length DFTs that cor...

In this paper, an approach is proposed to improve the numerical precision at the sound field simulation by the finite-difference time-domain (FDTD) method. The FDTD method is a numerical solution for the wave equation, proposed by R. Courant. Although it has achieved to simulate wave propagation by numerical solution for the wave equation, it causes numerical dispersions due to their approximat...

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...

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (WienerKhintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this probl...

Reconstruction of signals or images from a few discrete Fourier transform (DFT) values has applications in MRI and SAR. Many real-world signals can be sparsified by an invertible transformation, such as wavelets, into a sparse (mostly zero, with K nonzero values at unknown locations) signal. This Ksparse signal can be reconstructed using the K lowestfrequency DFT values using Prony’s method or ...

In this manuscript, density functional theory was used to explore structural, vibrational and optical properties of the (Sc2O3)n (n=1-5) cluster systems using DFT/B3LYP/LanL2DZ level of computation. Different stable isomers were obtained and numerous chemical parameters such as HOMO-LUMO gap, ionization potential and electron affinity were calculated successfully. Stability of the clusters was ...

In this paper, we propose a low-cost algorithm for recovering multitone signals from compressive measurements. We introduce a simple and efficient modification to orthogonal matching pursuit. Our approach uses a DFT basis, but refines the frequency estimate obtained at each iteration via a simple gradient descent. We find that by adapting the dictionary in this manner we can realize the benefit...