A group of MIT researchers will present a new algorithm at the Association for Computing Machinery’s ‘Symposium on Discrete Algorithms’ (SODA) this week, that in a large range of practically important cases, improves on the fast Fourier transform (FFT). 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 monthly bandwidth allotments.
Like the FFT, the new algorithm works on digital signals. The FFT takes a digital signal containing a certain number of samples and expresses it as the weighted sum of an equivalent number of frequencies.
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.