We encountered the Fourier series in passing in Chap. 5. Then it was just to illustrate the importance of sine waves as a fundamental waveform from which more complex ones such as a square wave could be constructed by adding them with different frequencies and amplitudes. Now we shall develop the formalism that, starting with an analytic function, we can replicate it by a series of waveforms – the Fourier series. We can well ask – why bother when we can just use an FFT? A good question! Is there a good answer?