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 versionof the Nearly Optimal sFFT algorithm for the noisy case, this modified algorithm solves the accuracy issues of the original version by modifying theflat window and the procedures; and second, we implemented the modifiedalgorithm on a multicore platform composed of eight cores. The experi-mental results on the cluster indicate that the developed implementation isfaster 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 ofthe authors,the developed implementation is the first one of the Nearly Optimal sFFT algorithm for the noisy case.
Highlights
Researchers from the Massachusetts Institute of Technology (MIT) presented two Sparse Fast Fourier Transform (sFFT) algorithms [2] which improve the runtime over all the previous developments [1],[5],[6],[7] including the most optimized conventional Fast Fourier Transform (FFT) algorithms like FFTW [8]; the first algorithm is intended for the noiseless case, and the second algorithm is intended for the noisy case
First, we developed some comparisons of sFFT-4.0 implementation against the previous sFFT implementations AAFFT and sFFT-2.0 in terms of runtime and accuracy versus Signal to Noise Ratio (SNR); and second, we present the achieved improvements when the multicore architecture is used for sFFT-4.0 implementation
In this paper we present a modified Nearly Optimal sFFT algorithm for the noisy case, this algorithm reduces the sampling cost and corrects the zero-hash issue of the original algorithm by doubling the bandwidth of the flat window and by modifying the original procedures
Summary
To the best of our knowledge there are only four software implementations of the MIT sFFT algorithms reported in literature; the first one was developed by the algorithm authors for the first version of the sFFT algorithm [1]; the second one is an optimized implementation of |74. There is no software implementation reported in literature of the Nearly Optimal sFFT algorithm for the noisy case, which is of practical interest for scientific researchers. The modified algorithm has an improved accuracy when compared with the original version described in [2], by modifying the flat window and the procedures; to the best of our knowledge, the modified algorithm is the first implementation of the Nearly Optimal sFFT algorithm for the noisy case, and it is very suitable for hardware implementation using ASICs or FPGAs
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