An Adaptive Tuning Sparse Fast Fourier Transform

Abstract

The Sparse Fast Fourier Transform (SFFT) is a novel algorithm for discrete Fourier transforms on signals with the sparsity in frequency domain. A reference implementation of the algorithm has been proven to be faster than modern FFT library in cases of sufficient sparsity. However, the SFFT implementation has the drawback that it only works reliably for very specific input parameters, especially signal sparsity k. This drawback hinders the extensive applications of SFFT. In this paper, we present a new Adaptive Tuning Sparse Fast Fourier Transform (ATSFFT). In the case of unknown sparsity k, ATSFFT can probe the sparsity k via adaptive dynamic tuning technology and then complete the Fourier transform of signal. Experimental results show that ATSFFT not only can control the error better than SFFT, but also performs faster than SFFT, which computes more efficiently than the state-of-the-art FFTW.