We can create an encoding scheme in the frequency domain to represent an alphabet of letters. But, as this information-encoding scheme stands, we can represent one letter for all time. However, we note that the Fourier coefficients depend only on the signal's characteristics over a single period. We could change the signal's spectrum every T T as each letter is typed. In this way, we turn spectral coefficients on and off as letters are typed, thereby encoding the entire typed document. For the receiver (see the Fundamental Model of Communication) to retrieve the typed letter, it would simply use the Fourier formula for the complex Fourier spectrum for each T T -second interval to determine what each typed letter was. Figure 1 shows such a signal in the time-domain.

In this Fourier-series encoding scheme, we have used the fact that spectral coefficients can be independently specified and that they can be uniquely recovered from the time-domain signal over one "period." Do note that the signal representing the entire document is no longer periodic. By understanding the Fourier series' properties (in particular that coefficients are determined only over a T T -second interval, we can construct a communications system. This approach represents a simplification of how modern modems represent text so that they can be transmitted over telephone lines.