Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case
Main Article Content
Keywords
Sparse Fourier Transform, multicore programming, computer cluster
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.
MSC: 65T50
Downloads
References
[2] ——, “Nearly optimal sparse Fourier transform,” in Proceedings of the 44th symposium on Theory of Computing (STOC), New York, USA, May 2012. pp. 563–578.
[3] P. Indyk, M. Kapralov, and and Eric Price, “(Nearly) Sample-Optimal Sparse Fourier Transform,” in ACM-SIAM Symposium on Discrete Algorithms (SODA), Portland, USA, 2014.
[4] H. Hassanieh, L. Shi, O. Abari, E. Hamed, and D. Katabi, “GHz-wide sensing and decoding using the sparse Fourier transform,” in INFOCOM, 2014 Proceedings IEEE. IEEE, 2014, pp. 2256–2264. [Online]. Available: http://dx.doi.org/10.1109/INFOCOM.2014.6848169
[5] A. C. Gilbert, S. Muthukrishnan, and M. J. Strauss, “Improved time bounds for near-optimal sparse Fourier representations,” in Proceedings of SPIE Wavelets XI, San Diego, USA, 2005, pp. 1–15.
[6] A. C. Gilbert, Y. Li, E. Porat, and M. J. Strauss, “Approximate sparse recovery: optimizing time and measurements,” in Proceedings of the 42nd ACM symposium on Theory of computing, Cambridge, USA, 2012.
[7] A. C. Gilbert, M. J. Strauss, and J. A. Tropp, “A Tutorial on Fast Fourier Sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 57–66, 2008. [Online]. Available: http://dx.doi.org/10.1109/MSP.2007.915000
[8] M. Frigo and S. G. Johnson, FFTW, 3rd ed., Massachusetts Institute of Technology, 2012. [Online]. Available: http://www.fftw.org/
[9] C. Wang, M. Araya-Polo, S. Chandrasekaran, A. St-Cyr, B. Chapman, and D. Hohl, “Parallel Sparse FFT,” in Proceedings of the 3rd Workshop on Irregular Applications: Architectures and Algorithms,
New York, NY, USA, 2013, pp. 10:1—-10:8. [Online]. Available: http://dx.doi.org/10.1145/2535753.2535764
[10] J. Hu, Z. Wang, Q. Qiu, W. Xiao, and D. J. Lilja, “Sparse Fast Fourier Transform on GPUs and Multi-core CPUs,” in Computer Architecture and High Performance Computing (SBAC-PAD), 2012 IEEE
24th International Symposium on, Oct. 2012, pp. 83–91. [Online]. Available: http://dx.doi.org/10.1109/SBAC-PAD.2012.34
[11] J. Schumacher, “High Performance Sparse Fast Fourier Transform,” Master Thesis, ETH Zurich, Department of Computer Science, 2013. [Online]. Available: http://goo.gl/3alHvS
[12] A. Dutt and V. Rokhlin, “Fast Fourier transforms for nonequispaced data, II,” Applied and Computational Harmonic Analysis, vol. 2, no. 1, pp. 85–100, 1995. [Online]. Available: http://dx.doi.org/10.1006/acha.1995.1007
[13] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th ed. Washington, DC, USA: Dover, 1972.
[14] OpenMP, OpenMP Application Program Interface, OpenMP Architecture Review Board Std., 2013.