In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions include, e.g., the oft-considered set of block frequency sparse functions of the form
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best s-term approximation of the Discrete Fourier Transform (DFT)f ∈ C N of any given input vector f ∈ C N in just (s log N ) O(1) -time using only a similarly small number of entries of f . In particular, we present a deterministic SFT algorithm which is guaranteed to always recover a near best s-term approximation of the DFT of any given input vector f ∈ C N in O s 2 log 11 2 (N )time. Unlike previous deterministic results of this kind, our deterministic result holds for both arbitrary vectors f ∈ C N and vector lengths N . In addition to these deterministic SFT results, we also develop several new publicly available randomized SFT implementations for approximately computingf from f using the same general techniques. The best of these new implementations is shown to outperform existing discrete sparse Fourier transform methods with respect to both runtime and noise robustness for large vector lengths N . 2 ∩Z, by sampling its associated trigonometric polynomial f (x) = ω∈Bf ω e iωx
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.