In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any timevarying or spatialvarying quantity.
In the physical world, any quantity measurable through time or over space can be taken as a signal. Within a complex society, any set of human information or machine data can also be taken as a signal. Such information or machine data (for example, the dots on a screen, the ink making up text on a paper page, or the words now flowing into the reader's mind) must all be part of systems existing in the physical world – either living or nonliving.
Despite the complexity of such systems, their outputs and inputs can often be represented as simple quantities measurable through time or across space. In the latter half of the 20th century, electrical engineering itself separated into several disciplines, specializing in the design and analysis of physical signals and systems, on the one hand, and in the functional behavior and conceptual structure of the complex human and machine systems, on the other. These engineering disciplines have led the way in the design, study, and implementation of systems that take advantage of signals as simple measurable quantities in order to facilitate the transmission, storage, and manipulation of information.
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Definitions specific to subfields are common. For example, in information theory, a signal is a codified message, that is, the sequence of states in a communication channel that encodes a message.
In the context of signal processing, arbitrary binary data streams are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.
In a communication system, a transmitter encodes a message into a signal, which is carried to a receiver by the communications channel. For example, the words "Mary had a little lamb" might be the message spoken into a telephone. The telephone transmitter converts the sounds into an electrical voltage signal. The signal is transmitted to the receiving telephone by wires; and at the receiver it is reconverted into sounds.
In telephone networks, signalling, for example common channel signalling, refers to phone number and other digital control information rather than the actual voice signal.
Signals can be categorized in various ways. The most common distinction is between discrete and continuous spaces that the functions are defined over, for example discrete and continuous time domains. Discretetime signals are often referred to as time series in other fields. Continuoustime signals are often referred to as continuous signals even when the signal functions are not continuous; an example is a squarewave signal.
A second important distinction is between discretevalued and continuousvalued. Digital signals are sometimes defined as discretevalued sequencies of quantified values, that may or may not be derived from an underlying continuousvalued physical process. In other contexts, digital signals are defined as the continuoustime waveform signals in a digital system, representing a bitstream. In the first case, a signal that is generated by means of a digital modulation method is considered as converted to an analog signal, while it is considered as a digital signal in the second case.
If for a signal, the quantities are defined only on a discrete set of times, we call it a discretetime signal. In other words, a discretetime real (or complex) signal can be seen as a function from the set of integers to the set of real (or complex) numbers.
A continuoustime real (or complex) signal is any realvalued (or complexvalued) function which is defined for all time t in an interval, most commonly an infinite interval.
Less formally than the theoretical distinctions mentioned above, two main types of signals encountered in practice are analog and digital. In short, the difference between them is that digital signals are discrete and quantized, as defined below, while analog signals possess neither property.
One of the fundamental distinctions between different types of signals is between continuous and discrete time. In the mathematical abstraction, the domain of a continuoustime (CT) signal is the set of real numbers (or some interval thereof), whereas the domain of a discretetime (DT) signal is the set of integers (or some interval). What these integers represent depends on the nature of the signal.
DT signals often arise via sampling of CT signals. An audio signal, for example consists of a continually fluxuating voltage on a line that can be digitized by an ADC circuit, wherein the circuit will read the voltage level on the line, say, every 50 µs. The resulting stream of numbers are stored as digital data on a discretetime signal. Computers and other digital devices are restricted to discrete time.
If a signal is to be represented as a sequence of numbers, it is impossible to maintain arbitrarily high precision  each number in the sequence must have a finite number of digits. As a result, the values of such a signal are restricted to belong to a finite set; in other words, it is quantized.
Signals are often analyzed or modeled in terms of their frequency spectrum. Frequency domain techniques are applicable to all signals, both continuoustime and discretetime. If a signal is passed through an LTI system, the frequency spectrum of the resulting output signal is the product of the frequency spectrum of the original input signal and the frequency response of the system.
Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or information content.
