Another Sense of Fourier Transforms

So we've talked a lot about how telescopes (and, in fact, other optical systems) perform Fourier transforms of oncoming light waves. Interferometers function because the information in images tends to be concentrated in low-frequency/high-wavelength scales, so we can form a relatively complete image even if we aren't sampling every possible frequency. As it turns out, we can do pretty much the same thing to sound--and that's basically how mp3s work.

When you create a CD-quality recording of an audio track, each minute is about 10 megabytes of data. That may not sound like a lot now that everyone is packing terabyte hard drives, but it would still put a pretty serious strain on the tubes if everyone were downloading CD-quality music all the time. To allow us to compress audio files, the process of creating mp3s uses Fourier transforms to split a track up into 576 frequency bands. Within each of these bands, everything that is inaudible to humans is thrown away.

Fourier transforms allow us to store sound simply by tracking the intensities of different frequencies (Source).

Combined with other techniques, Fourier transforms allow us to take those 10 megabytes/minute of CD-quality audio and compress it down to 1 megabyte. Without them, the digital music industry probably just wouldn't exist.