Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Fast computation of magnetostatic fields by Non-uniform Fast Fourier Transforms

Abstract: The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results.

Accurate estimation method of sinusoidal frequency based on FFT

Abstract: In order to further improve the estimation precision of sinusoidal frequency, a new estimation method based on Fast Fourier Transform (FFT) is proposed. Zero-padding is used before the coarse estimation. And three sample values of Discrete-Time Fourier Transform (DTFT) of the original signal is used to perform the fine estimation. In the computer simulations, it can be shown that the proposed estimation method follows the Cramer-Rao Bound in the whole region of frequency offset. The estimation precision is higher than the existing estimators. The proposed estimator has low SNR threshold, and outperforms the existing estimators.

Fast Gauss transforms with complex parameters using NFFTs

Abstract: at the target knots yj ∈ [− 4 , 14 ], j = 1, . . . ,M , where σ = a + ib, a > 0, b ∈ R denotes a complex parameter. Fast Gauss transforms for real parameters σ were developed, e.g., in [15, 8, 9]. In [12], we have specified a more general fast summation algorithm for the Gaussian kernel. Recently, a fast Gauss transform for complex parameters σ with arithmetic complexity O(N logN +M) was introduced by Andersson and Beylkin [1]. In this paper, we show how our general fast summation algorithm developed in [11, 12, 6] can be specified for the Gaussian kernel with complex parameter σ to obtain a fast Gauss transform with arithmetic complexity O(N+M). This results in a simpler algorithm than those in [1] with competitive performance in practice. We prove error estimates concerning the dependence of the computational speed on the desired accuracy and the parameters a and |σ|. The heart of our algorithm is the discrete Fourier transform for non equispaced knots (NDFT), i.e., the evaluation of

An Optimal Algorithm for Computing Fourier Texture Descriptors

Abstract: The description of texture is an important problem in image analysis. Several methods in the literature require that local two-dimensional discrete Fourier transforms be computed as a first step in the texture description process. A chief limitation in these approaches has been the computational complexity of the transform calculation which has tended to limit the resolution of subsequent description and/or segmentation. It is shown here that through a suitable ordering of calculations, the transforms over a complete set of overlapping "texture windows" can be obtained efficiently. An algorithm is given and is shown to be time-optimal to within a constant factor.

Back-projection SAR imaging using FFT

Abstract: This paper describes a novel method based on the back-projection approach to generate SAR images. The back-projection operation has various “fast” implementations all using multilevel algorithms. In this paper a back-projection algorithm using the Fast Fourier Transform (FFT) is proposed. The basic method does not employ interpolation by using non uniform sampling, and it obtains the same results as the straightforward computation, with O(N^2logN) instead of O(N^4) complexity. This method is optimal for SPOT mode and for wide-band scenarios, however to expand the algorithm flexibility two additional implementations are presented. As opposed to the basic method which does not use interpolation at all, these implementations require interpolation in the imaging process, but the error introduced is negligible.