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whatever you think of wikipedia

it has a decent page with the Fourier transform equation...see link. The function f(t) merely has to be square-integrable, it does not have to be periodic, so an aperiodic or a random function can certainly be represented by an integral of sines and cosines. Now, an integral of sines and cosines is not exactly the same as a sum of sines and cosines and maybe that is the distinction you are making. I'm not sure. The Fourer series sum can only represent periodic functions. It's a pretty good article.


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