How do discrete signals differ from continuous signals?
Consider a simple telephone conversation: A person (message source) speaks into a telephone receiver (encoder), which converts the sound of the spoken word into an electrical signal. This electrical signal is then transmitted over telephone lines (channel) subject to interference (noise). When the signal reaches the telephone receiver (decoder) at the other end of the line it is converted back into vocal sounds. Finally, the recipient (message receiver) hears the original message.
In the context of information theory, the primary difference between discrete and continuous signals lies in the range of values they can represent.1
- Discrete signals are characterized by their ability to represent only a finite number of distinct, recognizable states. A common example is the English alphabet, where each letter serves as a discrete unit.1
- Continuous signals, often referred to as analog signals, represent quantities that can vary across an infinite set of values. Sound is a typical example of a phenomenon transmitted via continuous signals.1
While these two types of communication are fundamentally different, they are closely related in practice. Continuous signals can be approximated by discrete signals by increasing the number of available distinct values until any resulting inaccuracy falls below the level of perception or interest, a process utilized in technologies like compact discs and digital telecommunication systems. Mathematically, continuous signals are often analyzed using Fourier analysis, which models signals as a sum of simpler sine waves.21