Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Rapid computation of the discrete Fourier transform
SIAM Journal on Scientific Computing
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Explicit constructions of selectors and related combinatorial structures, with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Short Note: The type 3 nonuniform FFT and its applications
Journal of Computational Physics
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
A note on compressed sensing and the complexity of matrix multiplication
Information Processing Letters
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We study the problem of estimating the best B term Fourier representation for a given frequency-sparse signal (i.e., vector) A of length N ≫ B. More precisely, we investigate how to deterministically identify B of the largest magnitude frequencies of Â, and estimate their coefficients, in polynomial (B, log N) time. Randomized sub-linear time algorithms, which have a small (controllable) probability of failure for each processed signal, exist for solving this problem. However, for failure intolerant applications such as those involving mission-critical hardware designed to process many signals over a long lifetime, deterministic algorithms with no probability of failure are highly desirable. In this paper we build on the deterministic Compressed Sensing results of Cormode and Muthukrishnan (CM) [26, 6, 7] in order to develop the first known deterministic sub-linear time sparse Fourier Transform algorithm suitable for failure intolerant applications. Furthermore, in the process of developing our new Fourier algorithm, we present a simplified deterministic Compressed Sensing algorithm which improves on CM's algebraic compressibility results while simultaneously maintaining their results concerning exponential decay.