“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International SymposiumIaşi, România, May 27, 2005Flexible algorithm for FFT parallel implementationCornelia Victoria Anghel 1 , Darian Onchiş 21 PhD, Computers Science Department, “Eftimie Murgu” University, Reşiţa, 1700, Romania2 Computers Science Department, “Eftimie Murgu” University, Reşiţa, 1700, RomaniaSummaryFor the parallel execution on distributed memory Linux clusters, the FastFourier Transform algorithm (FFT) is partitioned into a number of processeswhich concurrently run on the available processors of the system. The analysis ofsequential algorithm points out different types of data dependencies that areremoved by insertion of synchronization points between processes. For the parallelalgorithm, an estimation of its runtime parameters is done in order to determinethe performance of the parallel execution.KEYWORDS: Fast Fourier Transform, implementation in parallel algorithm.1. INTRODUCTIONThe Fast Fourier Transform algorithm (FFT) is one of the most usefulalgorithm in digital signals processes applications: audio processing, imagesprocessing, statistic and scientific applications, and so on.This paper presents an eloquent example of a parallel multiprocessorsystem, which is implemented by the flexible FFT algorithm.So, a number of points are considered, like, X = (X[0], X[1], … X[n – 1]),the Discrete Fourier Transform become a sequence Y = (Y[0], Y[1], …Y[n – 1]),with same n dimension, in that the elements Y[i], have the expression:, 0 ≤i < n (1)where is the n solution from the complex plane. From relation (1)results that the evaluation for each element Y[i], need n complex operations, so theexecution time for all n points with Discrete Fourier Transform (DFT) is O(n 2 ).The FFT algorithm reduce this execution time at O(nlogn).To obtain this algorithm each element who has n DFT points is written likesum of two elements, with n/2 points DFT, each, relation (2):