Signal (electrical engineering)

In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying 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 non-living.

Despite the complexity and even mystery – in the case of the reader's mind – of such systems, their outputs and inputs can often be represented with great fidelity 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.

ome definitions

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 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.

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. Discrete-time signals are often referred to as "time series" in other fields. Continuous-time signals are often referred to as "continuous signals" even when the signal functions are not continuous; an example is a square-wave signal.

A second important distinction is between discrete-valued and continuous-valued. Digital signals are discrete-valued, but are often derived from an underlying continuous-valued physical process.

Discrete-time and continuous-time signals

If for a signal, the quantities are defined only on a discrete set of times, we call it a discrete-time signal. In other words, a discrete-time real (or complex) signal can be seen as a function from the set of integers to the set of real (or complex) numbers.

A continuous-time real (or complex) signal is any real-valued (or complex-valued) function which is defined for all time "t" in an interval, most commonly an infinite interval.

Analog and digital signals

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.

Discretization

One of the fundamental distinctions between different types of signals is between continuous and discrete time. In the mathematical abstraction, the domain of a continuous-time (CT) signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (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 discrete-time signal. Computers and other digital devices are restricted to discrete time.

Quantization

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.

Examples of signals

* "Motion". The motion of a particle through some space can be considered to be a signal, or can be represented by a signal. The domain of a motion signal is one-dimensional (time), and the range is generally three-dimensional. Position is thus a 3-vector signal; position and orientation is a 6-vector signal.
* "Sound". Since a sound is a vibration of a medium (such as air), a sound signal associates a pressure value to every value of time and three space coordinates. A microphone converts sound pressure at some place to just a function of time, using a voltage signal as an analog of the sound signal.
* "Compact discs" (CDs). CDs contain discrete signals representing sound, recorded at 44,100 samples per second. Each sample contains data for a left and right channel, which may be considered to be a 2-vector (since CDs are recorded in stereo).
* "Pictures". A picture assigns a color value to each of a set of points. Since the points lie on a plane, the domain is two-dimensional. If the picture is a physical object, such as a painting, it's a continuous signal. If the picture is a digital image, it's a discrete signal. It's often convenient to represent color as the sum of the intensities of three primary colors, so that the signal is vector-valued with dimension three.
* "Videos". A video signal is a sequence of images. A point in a video is identified by its position (two-dimensional) and by the time at which it occurs, so a video signal has a three-dimensional domain. Analog video has one continuous domain dimension (across a scan line) and two discrete dimensions (frame and line).
* Biological "membrane potentials". The value of the signal is a straightforward electric potential ("voltage"). The domain is more difficult to establish. Some cells or organelles have the same membrane potential throughout; neurons generally have different potentials at different points. These signals have very low energies, but are enough to make nervous systems work; they can be measured in aggregate by the techniques of electrophysiology.

Frequency analysis

Signals are often analyzed or modeled in terms of their frequency spectrum. Frequency domain techniques are applicable to all signals, both continuous-time and discrete-time. 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.

Entropy

Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or "information content".

ee also

*Impulse function
*Signal noise
*Signal to noise ratio
*Signal processing
**Digital signal processing
*Image processing
**Digital image processing
* Wikibook

Works cited

*Hsu, P. H. "Schaum's Theory and Problems: Signals and Systems", McGraw-Hill 1995, ISBN 0-07-030641-9
*Lathi, B.P., "Signal Processing & Linear Systems", Berkeley-Cambridge Press, 1998, ISBN 0-0941413-35-7
*Shannon, C. E., 2005 [1948] , "A Mathematical Theory of Communication," ( [http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html corrected reprint] ), accessed Dec. 15, 2005. Orig. 1948, "Bell System Technical Journal", vol. 27, pp. 379-423, 623-656.