The original Fourier Transform as invented by the
smart French
guy of the same name does operate on continuous (as opposed to
sampled) data from -inf to +inf.
I understand Fourier invented the Fourier Series "only", anyone knows
who generalized it to FT?
And yes, I think the FT isn't so hard to understand, and a pretty
useful concept. FFT, on the other hand... never really tried.
Greetings