Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Data driven signal processing: an approach for energy efficient computing
ISLPED '96 Proceedings of the 1996 international symposium on Low power electronics and design
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Efficient Similarity Search In Sequence Databases
FODO '93 Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms
Some topics in analysis of boolean functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Combinatorial Sublinear-Time Fourier Algorithms
Foundations of Computational Mathematics
Fast approximate correlation for massive time-series data
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
A New Flexible Filter Bank for Low Complexity Spectrum Sensing in Cognitive Radios
Journal of Signal Processing Systems
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Nearly optimal sparse fourier transform
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Supervised dictionary learning for music genre classification
Proceedings of the 2nd ACM International Conference on Multimedia Retrieval
Faster GPS via the sparse fourier transform
Proceedings of the 18th annual international conference on Mobile computing and networking
A framework for low-communication 1-D FFT
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Bilingual analysis of song lyrics and audio words
Proceedings of the 20th ACM international conference on Multimedia
Proceedings of the 14th Workshop on Mobile Computing Systems and Applications
Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform
Proceedings of the 32nd symposium on Principles of database systems
Invariant object recognition using radon and fourier transforms
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
Illumination invariant face recognition
ICIC'13 Proceedings of the 9th international conference on Intelligent Computing Theories
IA^3 '13 Proceedings of the 3rd Workshop on Irregular Applications: Architectures and Algorithms
Expert Systems with Applications: An International Journal
A framework for low-communication 1-D FFT
Scientific Programming - Selected Papers from Super Computing 2012
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We consider the sparse Fourier transform problem: given a complex vector x of length n, and a parameter k, estimate the k largest (in magnitude) coefficients of the Fourier transform of x. The problem is of key interest in several areas, including signal processing, audio/image/video compression, and learning theory. We propose a new algorithm for this problem. The algorithm leverages techniques from digital signal processing, notably Gaussian and Dolph-Chebyshev filters. Unlike the typical approach to this problem, our algorithm is not iterative. That is, instead of estimating "large" coefficients, subtracting them and recursing on the reminder, it identifies and estimates the k largest coefficients in "one shot", in a manner akin to sketching/streaming algorithms. The resulting algorithm is structurally simpler than its predecessors. As a consequence, we are able to extend considerably the range of sparsity, k, for which the algorithm is faster than FFT, both in theory and practice.