Signal (information theory)

A signal is an abstract element of information, or (more commonly) a flow of information (in one or more dimensions). A two-dimensional signal is usually called an image.

More technically, a signal is any physical phenomenon that can be modeled as a function from time or position to some real- or vector-valued domain, and is used to carry information. A signal is said to be analog, if the domain and range are continuous; or digital, when both sides are better modeled as discrete sets. (Sometimes one needs to consider signals that are discrete only on one side, i.e. discrete-time signals or discrete-valued signals.)

A typical signal is sound such as speech whereby the signal carries the information of the spoken words, the identity of the speaker and for example, emotional cues. Another typical signal is a radio transmission which, in turn, can carry the speech sound-signal. Both sound and radio signals are analog signals.

Examples of digital signals include:

• written language, when encoded as data
• representations of analog signals within a digital framework
• computer generated signals.

Signal processing often uses operators that are time-invariant and linear (or nearly linear); for that reason, the frequency spectrum (or Fourier transform) plays an important role in the theory and applications. The frequency spectrum is a signature of the signal.

Another important propery of a signal (actually, of a statistically defined class of signals) is its entropy or information contents, measured in bits (or bits per second, or bits per square millimeter, etc.).

See noise (physics), signal to noise ratio, signal processing, image processing