Leaner Fourier transforms
The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing. The algorithm allowed computers to quickly perform Fourier transforms — fundamental operations that separate signals into their individual frequencies — leading to developments in audio and video engineering and digital data compression.But ever since its development in the 1960s, computer scientists have been searching for an algorithm to better it.Last year MIT researchers Piotr Indyk and Dina Katabi did just that, unveiling an algorithm that in some circumstances can perform Fourier transforms hundreds of times more quickly than the fast Fourier transform (FFT). Now Indyk, a professor of computer science and engineering and a member of the Theory of Computation Group within the Computer Science and Artificial Intelligence Laboratory (CSAIL), and his team have gone a step further, significantly reducing the number of samples that must be taken from a given signal in...