Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case

Abstract

In this paper we present an optimized software implementation (sFFT-4.0) of the recently developed Nearly Optimal Sparse Fast Fourier Transform (sFFT) algorithm for the noisy case. First, we developed a modified version of the Nearly Optimal sFFT algorithm for the noisy case, this modified algorithm solves the accuracy issues of the original version by modifying the flat window and the procedures; and second, we implemented the modified algorithm on a multicore platform composed of eight cores. The experimental results on the cluster indicate that the developed implementation is faster than direct calculation using FFTW library under certain conditions of sparseness and signal size, and it improves the execution times of previous implementations like sFFT-2.0. To the best knowledge of the authors, the developed implementation is the first one of the Nearly Optimal sFFT algorithm for the noisy case. Implementación software eficiente de la Transformada de Fourier Escasa casi óptima para el caso con ruido ResumenEn este artículo se presenta una implementación software optimizada (sFFT-4.0) del algoritmo Transformada Rápida de Fourier Escasa (sFFT) Casi Óptimo para el caso con ruido. En primer lugar, se desarrolló una versión modificada del algoritmo sFFT Casi Óptimo para el caso con ruido, esta modificación resuelve los problemas de exactitud de la versión origial al modificar la ventana plana y los procedimientos; y en segundo lugar, se implementó el algoritmo modificado en una plataforma multinúcleo compuesta de ocho núcleos. Los resultados experimentales en el agrupamiento de computadores muestran que la implementación desarrollada es más rápida que el cálculo directo usando la biblioteca FFTW bajo ciertas condiciones de escasés y tamaño de señal, y mejora los tiempos de ejecución de implementaciones previas como sFFT-2.0. Al mejor conocimiento de los autores, la implementación desarrollada es la primera del algoritmo sFFT Casi Óptimo para el caso con ruido.Palabras clave: Transformada de Fourier Escasa; programación multi núcleo; agrupamiento de computadoras.

Empirical Evaluation of Typical Sparse Fast Fourier Transform Algorithms

“…After knowing the number of collisions, the aliasing problem is reformulated as Moment Preserving Problem(MPP). The orthogonal polynomial formula P (z) is defined as Equation (24) and P (z) ≈ 0. The Matrix M a ∈ C a×a is defined as Equation (25).…”

“…The paper [20] summarizes a three-step approach in the stage of spectrum reconstruction and provides a standard testing platform to evaluate different sFFT algorithms. There are also some researches try to conquer the sFFT problem from other aspects: complexity [21], [22], performance [23], [24], software [25], [26], hardware [27], higher dimensions [28], [29], implementation [30], [31] and special setting [32], [33] perspectives. This paper is structured as follows.…”

On Performance of Sparse Fast Fourier Transform Algorithms Using the Flat Window Filter

“…Based on the above-mentioned properties we get formula (20) If the set I is a set of coordinates position, the position f = (σ −1 u)modN ∈ I , suppose there is no hash collision in the bucket i, i = round(u/L), round() means to make decimals rounded. Through formula(20), we can get the formula (21)…”

“…The paper [17] proposes an overview of sFFT technology and summarizes a three-step approach in the stage of spectrum reconstruction and provides a standard testing platform that can be used to evaluate different sFFT algorithms. There are also some researches try to conquer the sFFT problem from a lot of aspects: computational complexity [18], [19], performance of the algorithm [20], [21], software [22], [23], higher dimensions [24], [25], implementation [26], hardware [27] and special setting [28], [29] perspectives.…”

On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

“…The paper [21] summarizes a three-step approach in the stage of spectrum reconstruction and provides a standard testing platform to evaluate different sFFT algorithms. There have also been some researches that tried to conquer the sFFT problem from other aspects: complexity [22,23], performance [24,25], software [26,27], hardware [28], higher dimensions [29,30], implementation [31,32], and special setting [33,34] perspectives.…”