Some people are able to do Fourier transforms without doing a single integral (i.e. just looking at a function). After thinking about it for a while I discovered that convolution is really helpful. For example, because two square waves are convolved to make a triangle wave, then the Fourier transform will be the Fourier transform of the square multiplied by the Fourier transform of the square. I am sure there are other methods though, does anybody know of anything better or any good tutorials of approximating the Fourier transform of functions?