This Topic introduces the Fourier transform as the limiting operation of taking a periodic signal, and sending the period to infinity, so as to represent a non-periodic signal. The Topic considers this by looking at a particular example, namely the periodic pulse wave, where the spectrum has an elegant shape that is easy to analyse. The properties of this spectrum are then considered as the period is increased. It is noticed that the shape of the spectrum doesn't change, but the gaps between the frequency components are filled in with more frequencies. In the limit, the discrete-spectrum becomes continuous. This phenomena is then investigated further using some MATLAB code that can simulate this process for different periodic waveforms. The limiting spectrum is the Fourier transform of the non-periodic signal.