If you understand the fourier transform, you should have some idea of its inverse. And that's exactly how (one part) of compressing an image or audio works. Yo

If you understand the fourier transform, you should have some idea of its inverse. And that's exactly how (one part) of compressing an image or audio works. You take a signal, take its fourier transform, and then cut off the frequencies above some threshold you don't care about (I'm ignoring certain complicating factors for simplicity). Let's say your original signal has frequencies up to 22KHz. If you're only interested in moderate fidelity human voices talking, maybe you cut off everything below 100 Hz and above 3.4 KHz. You just toss that information. Then on the receiving end, you do an inverse DFT and reconstruct the signal. JPG and MP3 do something like this, along with a pile of other tricks.