 The Fourier transform is an amazing tool, but it is only practical in situations where we know the equation describing our signal. We cannot calculate the Fourier transform of an arbitrary signal if it cannot be expressed as a mathematical equation. This is because the Fourier transform requires us to know what our signal is doing at every moment in time, forever. There are an infinite number of moments, even in a limited amount of time. In order to be practical, we can only look at the signal at discrete moments in time for a limited period. After all, none of us lives forever. This is where the discrete Fourier transform comes in useful. The DFT tests a sampled finite length signal and tells us, based on the sample points we gave it, which frequencies are present in that signal.