The faster-than-fast Fourier transform (MIT)
The Fourier transform is one of the most fundamental concepts in the
information sciences. It’s a method for representing an irregular signal —
such as the voltage fluctuations in the wire that connects an MP3 player to a
loudspeaker — as a combination of pure frequencies. It’s universal in signal
processing, but it can also be used to compress image and audio files, solve
differential equations and price stock options, among other things.
The reason the Fourier transform is so prevalent is an algorithm called the
fast Fourier transform (FFT), devised in the mid-1960s, which made it
practical to calculate Fourier transforms on the fly. Ever since the FFT was
proposed, however, people have wondered whether an even faster algorithm could
be found.
At the Symposium on Discrete Algorithms (SODA) this week, a group of MIT
researchers will present a new algorithm that, in a large range of practically
important cases, improves on the fast Fourier transform. Under some
circumstances, the improvement can be dramatic — a tenfold increase in speed.
The new algorithm could be particularly useful for image compression,
enabling, say, smartphones to wirelessly transmit large video files without
draining their batteries or consuming their …
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