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.

Two-step 1-D fast Fourier transform without inter-processor communications

Abstract: Computing the 1-D fast Fourier transform (FFT) using the conventional six-step FFT on parallel computers requires intensive all-to-all communication due to the necessity of transposing an array three times This all-to-all communication significantly reduces the performance of FFT in parallel systems In this paper, we present a two-step parallel algorithm for implementing the 1-D FFT without inter-processor communication, at the expense of extra computation as opposed to the conventional six-step FFT The advantage of the two-step FFT algorithm over its six-step counterpart becomes obvious in systems where the cost of computation is lower that of inter-processor communication The 32-node Beowulf cluster is such a system with fast 2 GHz processors but relatively slow inter-processor communication by using 100 Mbit/s network switches Our simulation results show that the two-step FFT algorithm without inter-processor communication outperforms the six-step 1-D FFT on this cluster

A fast implementation of Quasi-Newton LMS algorithm using FFT

Abstract: In this paper, a new efficient adaptive filtering algorithm belonging to the Quasi-Newton (QN) family is proposed. In the new algorithm, the autocorrelation matrix is assumed to be Toeplitz. Due to this assumption, the algorithm can be implemented in the frequency domain using the fast Fourier transform (FFT). The proposed algorithm turns out to be particularly suitable for adaptive channel equalization in wireless burst transmission systems. The algorithm exhibits a faster convergence rate and less computational complexity, as compared with other Newton-type algorithms. The performance of the proposed algorithm is compared to that of the QN-LMS algorithm in noise cancellation and channel equalization settings.

Streamlined real-factor FFTs

Abstract: In this paper we show that Rader and Brenner's ‘real-factor’ FFT can be streamlined so that it requires lower computational complexity as compared to the Cooley- Tukey radix-2 FFT. We then show that the fixed point implementation of ‘real-factor’ FFT can be modified so that its noise-to-signal ratio (NSR) is lower than the NSR of Cooley-Tukey radix-2 FFT. Finally simulation results are presented which verify the suitability of ‘real-factor’ FFTs.

Comparison of the reconstruction algorithms in digital micro-holography

Abstract: To improve the quality of the reconstructed image, the common used three reconstruction algorithms in digital holographic microscopy, Fresnel transform algorithm, angular spectrum algorithm, and convolution algorithm, all based on fast-Fourier-transform (FFT) are investigated and compared. By using off-axis lensless Fourier setup the digital hologram of a USAF test target is recorded and reconstructed numerically with the three algorithms at different reconstruction distances. The results show that by Fresnel transform algorithm the lensless Fourier transform digital hologram can be reconstructed at any distances. For convolution and angular spectrum algorithms, there is an optimal reconstruction distance. For convolution algorithm, when the reconstruction distance is different from the optimal distance, the image resolution is decreased, particularly for small distance. When the reconstructing distance is slightly smaller and very larger than the optimal one the high quality image can also be obtained by using angular spectrum algorithm. Angular spectrum algorithm is better than convolution algorithm. The Fresnel transform algorithm is the optimal numerical reconstruction algorithm in digital holographic microscopy.

2-D FFT algorithm by matrix factorization in a 2-D space

Abstract: A new 2-D FFT algorithm is described. This algorithm applies a 2-D matrix factorization technique in a 2-D space and offers a way to do 2-D FFT in both dimensions simultaneously. The computation is greatly reduced compared to traditional algorithms. This will improve the realization of a 2-D FFT on any kind of computer. However its good parallelism will especially benefit an implementation on a computer with hypercube architecture. A good arrangement of parallel processors will save a great deal of running time. Furthermore this algorithm can be extended toM-D cases forM>2.