So I'm doing an internship this summer and one of the things I have to be acquainted with is Fourier Transforms. My adviser gave me a simple example with that of sin(x). He said that what the Fourier Transform does is transform a time domain signal into one of a frequency signal. Essentially, he added, the peak of a Fourier Transform is that of the greatest match of the frequency to the function sin(x)--where points things that are closest to x-axis are the worst match. But since I've started this assignment earlier today, I've noticed that Mathematica does not plot Fourier Transform of functions such as sin(x) that have constant frequencies and periodicity for all x. Mathematica plots things such as sin(x)/x where the frequency isn't constant throughout the x-axis. Upon doing some research on FT, I suspect this is because Fourier Transform works for things that vary, not for functions that have constant periodicity. But I don't know any better so I'm asking for your input. It would also be helpful if someone can clarify the whole concept of Fourier Transforms and how it relates to statistics and data analysis.