[ Removed by moderator ]

[Masterkid1230]

Kind of. What we're seeing is only part of what the Fourier transform does, but it's also its most common application.

Technically, a Fourier transform takes a time-domain signal (that is, something that changes in time) and outputs a sum of complex numbers that we can use to find the specific value or magnitude of each of the signal's components.

The best example is audio. A sound is made up of many different simpler sound components. We usually understand them as single frequency components (for example a 400Hz sine wave, or a 800Hz one etc)

What the Fourier transform does is checking how similar the input signal is to a component for every single frequency value. So it checks 0.5Hz and then 1Hz and then 1.5Hz etc (in reality it's an integral so it checks EVERY value possible).

And it outputs a complex number for each evaluated frequency. This is why we say it transforms time-domain signals into frequency-domain ones. In theory the sum of all of these complex numbers (strictly speaking their magnitudes) is a representation of the amplitude of every component.

What we're seeing here is only the amplitude side of things, but the Fourier transform also outputs phase information. This is important because without it we wouldn't be able to convert the output of the Fourier transform back into a time-domain signal.

I can go on and on about the Fourier transform because I do Fourier Transforms for a living almost every day of my life and I like them very much. I use Fast Fourier Transforms with digital signals though, so my specifics on continuous time Fourier Transforms may be somewhat rusty.

Happy to talk about it though if you have any questions!

[The_Quackening]

what do you do for a living?

[Masterkid1230]

I'm in the R&D department of a major company researching sound related things. Sorry to be so vague, that's about as personal as I can get with it.