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posted by Fnord666 on Tuesday June 11 2019, @02:18PM   Printer-friendly
from the transformational-idea dept.

Submitted via IRC for Bytram

The Math Trick Behind MP3s, JPEGs, and Homer Simpson's Face

Over a decade ago, I was sitting in a college math physics course and my professor spelt out an idea that kind of blew my mind. I think it isn't a stretch to say that this is one of the most widely applicable mathematical discoveries, with applications ranging from optics to quantum physics, radio astronomy, MP3 and JPEG compression, X-ray crystallography, voice recognition, and PET or MRI scans. This mathematical tool—named the Fourier transform, after 18th-century French physicist and mathematician Joseph Fourier—was even used by James Watson and Francis Crick to decode the double helix structure of DNA from the X-ray patterns produced by Rosalind Franklin. (Crick was an expert in Fourier transforms, and joked about writing a paper called, "Fourier Transforms for birdwatchers," to explain the math to Watson, an avid birder.)

You probably use a descendant of Fourier's idea every day, whether you're playing an MP3, viewing an image on the web, asking Siri a question, or tuning in to a radio station. (Fourier, by the way, was no slacker. In addition to his work in theoretical physics and math, he was also the first to discover the greenhouse effect.)

So what was Fourier's discovery, and why is it useful?

The story provides great visual examples of how even complex waves can be approximated by a series of sine waves summed together. Further, the parameters to the sine waves and a much more concise description of the approximated item. Examples are given of a roughly-square wave. Another example uses circles instead of sine waves. A great YouTube video shows these in action.

Wish I had this available to me before I was taught FT and FFT in college!


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  • (Score: 0) by Anonymous Coward on Wednesday June 12 2019, @07:30AM

    by Anonymous Coward on Wednesday June 12 2019, @07:30AM (#854557)

    I excelled at puns - and that, Sir, was not a pun. Intended.