Improvement On Age-Old Mathematical Principle Could Yield Improved Images, Video | TechCrunch
Hardware Improvement On Age-Old Mathematical Principle Could Yield Improved Images, Video It’s not often that you improve on a bit of math that has been around for 200 years. The Fourier transform was first proposed in 1811 by a Frenchman named Joseph Fourier, though it wasn’t until the middle of the 20th century that he was given the credit he deserved. His technique broke down a complex signal i
Nearly Optimal Sparse Fourier Transform
We consider the problem of computing the k-sparse approximation to the discrete Fourier transform of an n-dimensional signal. We show: * An O(k log n)-time randomized algorithm for the case where the input signal has at most k non-zero Fourier coefficients, and * An O(k log n log(n/k))-time randomized algorithm for general input signals. Both algorithms achieve o(n log n) time, and thus improve ov
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