Here's a pretty good lecture on exactly that subject: https://www.rose-hulman.edu/~bryan/invprobs/jpegtalk2.pdf https://www.rose-hulman.edu/~bryan/invprobs/jpeg

Here's a pretty good lecture on exactly that subject: https://www.rose-hulman.edu/~bryan/invprobs/jpegtalk2.pdf https://www.rose-hulman.edu/~bryan/invprobs/jpegtalk2.pdf Honestly though, the Fourier transform is useful anywhere that it's easy to think in terms of frequency instead of time. 90% of use cases in the real world come about from trying to do something that's that's easy to express in terms of signal frequency and difficult to express in terms of signal time/space. You can just use the Fourier transform to convert between them efficiently. To give a morbid, but non-obvious example, I once did some work with a charity that was concerned with migrant deaths. They wanted to figure out where the migrants most at risk were working to approach the farmers hiring them directly. We got a dataset of when migrant bodies were found and did an FFT (among other processing) to find the periodicity of the crops that they were coming to harvest. There's only a few major crops and they tend to have distinct growing periods, so this is enough information to pinpoint certain crops like strawberries.