Improved Approximation Guarantees for Sublinear-Time Fourier Algorithms

ABSTRACT. In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings are developed. As a consequence, approximate Fourier transforms are obtained which will identify a near-optimal k-term Fourier series for any given input function, f : [0, 2]D C, in O k2

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: M. A. Iwen
• Keywords: CORR 2010, Education, Fourier Transforms, Sparse Fourier, Sparse Fourier Transform