Fast Fourier Transforms plays the magic role of simplifying not distorting reality. It should be every modeler’s dream coming through.
Last week at the Association for Computing Machinery’s Symposium on Discrete Algorithms (SODA) a new way of calculating Fast Fourier Transforms was presented by a group of MIT researchers. It’s possible that under certain situations it may be up to ten times faster than the current way we do these.
Here’s a quickie explainer: Fourier transforms are a mathematical trick to simplify how you represent a complicated signal–say the waves of sound made by speaking. They work by reducing the complex wave pattern to a simple and pretty short list of numbers that, when run through the system again, result in a very good approximation of the original signal.
You’re certainly familiar with a type of image format called JPEG. They’re much smaller than other sorts of digital image format, which is why they’re used all over web pages