The December 2022 issue of IEEE Spectrum is here!

Close bar

A Faster Fast Fourier Transform

New algorithm crunches sparse data with speed

3 min read
A Faster Fast Fourier Transform

trans01

Images and analysis: Steve Haroz
Everyday Sparsity: Natural signals [top] are often “sparse,” which means they have relatively few frequency components of significance. A random image [bottom], however, contains significant components at all frequencies. The new fast Fourier transform algorithm accelerates calculations on sparse signals only.
Click on image for a larger view.

Gilbert Strang, author of the classic textbook Linear Algebra and Its Applications, once referred to the fast Fourier transform, or FFT, as “the most important numerical algorithm in our lifetime.” No wonder. The FFT is used to process data throughout today’s highly networked, digital world. It allows computers to efficiently calculate the different frequency components in time-varying signals—and also to reconstruct such signals from a set of frequency components. You couldn’t log on to a Wi-Fi network or make a call on your cellphone without it. So when some of Strang’s MIT colleagues announced in January at the ACM-SIAM Symposium on Discrete Algorithms that they had developed ways of substantially speeding up the calculation of the FFT, lots of people took notice. 


Keep Reading ↓Show less

This article is for IEEE members only. Join IEEE to access our full archive.

Join the world’s largest professional organization devoted to engineering and applied sciences and get access to all of Spectrum’s articles, podcasts, and special reports. Learn more →

If you're already an IEEE member, please sign in to continue reading.

Membership includes:

  • Get unlimited access to IEEE Spectrum content
  • Follow your favorite topics to create a personalized feed of IEEE Spectrum content
  • Save Spectrum articles to read later
  • Network with other technology professionals
  • Establish a professional profile
  • Create a group to share and collaborate on projects
  • Discover IEEE events and activities
  • Join and participate in discussions

Why Functional Programming Should Be the Future of Software Development

It’s hard to learn, but your code will produce fewer nasty surprises

11 min read
Vertical
A plate of spaghetti made from code
Shira Inbar
DarkBlue1

You’d expectthe longest and most costly phase in the lifecycle of a software product to be the initial development of the system, when all those great features are first imagined and then created. In fact, the hardest part comes later, during the maintenance phase. That’s when programmers pay the price for the shortcuts they took during development.

So why did they take shortcuts? Maybe they didn’t realize that they were cutting any corners. Only when their code was deployed and exercised by a lot of users did its hidden flaws come to light. And maybe the developers were rushed. Time-to-market pressures would almost guarantee that their software will contain more bugs than it would otherwise.

Keep Reading ↓Show less
{"imageShortcodeIds":["31996907"]}