Signal (electrical engineering)
A signal as referred to in communication systems, signal processing, and electrical engineering "is a function that conveys information about the behavior or attributes of some phenomenon". In the physical world, any quantity exhibiting variation in time or variation in space (such as an image) is potentially a signal that might provide information on the status of a physical system, or convey a message between observers, among other possibilities. The IEEE Transactions on Signal Processing elaborates upon the term "signal" as follows:
Other examples of signals are the output of a thermocouple, which conveys temperature information, and the output of a pH meter which conveys acidity information. Typically, signals are often provided by a sensor, and often the original form of a signal is converted to another form of energy using a transducer. For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse.
The formal study of the information content of signals is the field of information theory. The information in a signal is usually accompanied by noise. The term noise usually means an undesirable random disturbance, but is often extended to include unwanted signals conflicting with the desired signal (such as crosstalk). The prevention of noise is covered in part under the heading of signal integrity. The separation of desired signals from a background is the field of signal recovery, one branch of which is estimation theory, a probabilistic approach to suppressing random disturbances.
Engineering disciplines such as electrical engineering have led the way in the design, study, and implementation of systems involving transmission, storage, and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines, specialising in the design and analysis of systems that manipulate physical signals; electronic engineering and computer engineering as examples; while design engineering developed to deal with functional design of man–machine interfaces.
Signal processing 
A typical role for signals is in signal processing. A common example is signal transmission between different locations. The embodiment of a signal in electrical form is made by a transducer that converts the signal from, whatever is, its original form to a waveform expressed as a current (I) or a voltage (V), or an electromagnetic waveform, for example, an optical signal or radio transmission. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as electronic amplifiers and electronic filters, and can be transmitted to a remote location by electronic transmitters and received using electronic receivers.
Some 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 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.
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 sometimes defined as discrete-valued sequencies of quantified values, that may or may not be derived from an underlying continuous-valued physical process. In other contexts, digital signals are defined as the continuous-time waveform signals in a digital system, representing a bit-stream. 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.
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. A simple source for a discrete time signal is the sampling of a continuous signal, approximating the signal by a sequence of its values at particular time instants.
A discrete-time real (or complex) signal can be seen as a function from (a subset of) the set of integers (the index labeling time instants) to the set of real (or complex) numbers (the function values at those instants).
A continuous-time real (or complex) signal is any real-valued (or complex-valued) function which is defined at every 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. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. 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 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 (discrete time) signals often arise via sampling of CT (continuous time) signals, for example, a continually fluctuating voltage on a line that can be digitized by an analog-to-digital converter circuit, wherein the circuit will read the voltage level on the line, say, every 50 microseconds. The resulting stream of numbers is stored as digital data on a discrete-time 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.
Examples of signals 
Signals in nature can be converted to electronic signals by various sensors. Some examples are:
- Motion. The motion of an object can be considered to be a signal, and can be monitored by various sensors to provide electrical signals. For example, radar can provide an electromagnetic signal for following aircraft motion. A motion signal is one-dimensional (time), and the range is generally three-dimensional. Position is thus a 3-vector signal; position and orientation of a rigid body is a 6-vector signal. Orientation signals can be generated using a gyroscope.
- 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 sound signal is converted to an electrical signal by a microphone, generating a voltage signal as an analog of the sound signal, making the sound signal available for further signal processing. Sound signals can be sampled at a discrete set of time points; for example, compact discs (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 signal (since CDs are recorded in stereo). The CD encoding is converted to an electrical signal by reading the information with a laser, converting the sound signal to an optical signal.
- Images. A picture or image consists of a brightness or color signal, a function of a two-dimensional location. The object's appearance is presented as an emitted or reflected electromagnetic wave, one form of electronic signal. It can be converted to voltage or current waveforms using devices such as the charge-coupled device. A 2D image can have a continuous spatial domain, as in a traditional photograph or painting; or the image can be discretized in space, as in a raster scanned digital image. Color images are typically represented as a combination of images in 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 two-dimensional position 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 an 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.
Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or information content.
See also 
|Wikibooks has a book on the topic of: Signals and Systems|
- Impulse function
- Signal noise
- Signal to noise ratio
- Signal processing
- Image processing
- Roland Priemer (1991). Introductory Signal Processing. World Scientific. p. 1. ISBN 9971509199.
- Some authors do not emphasize the role of information in the definition of a signal. For example, see Priyabrata Sinha (2009). Speech processing in embedded systems. Springer. p. 9. ISBN 0387755802. "To put it very generally, a signal is any time-varying physical quantity."
- "Aims and scope". IEEE Transactions on Signal Processing (IEEE).
- T. H. Wilmshurst (1990). Signal Recovery from Noise in Electronic Instrumentation (2nd ed.). CRC Press. pp. 11 ff. ISBN 0750300582.
- For an example from robotics, see K Nishio and T Yasuda (2011). "Analog–digital circuit for motion detection based on vertebrate retina and its application to mobile robot". In Bao-Liang Lu, Liqing Zhang, James Kwok. Neural Information Processing: 18th International Conference, Iconip 2011, Shanghai, China, November 13-17, 2011. Springer. pp. 506 ff. ISBN 3642249647.
- For example, see M. N. Armenise, Caterina Ciminelli, Francesco Dell'Olio, Vittorio Passaro (2010). "§4.3 Optical gyros based on a fiber ring laser". Advances in Gyroscope Technologies. Springer. p. 47. ISBN 364215493X.
- The optical reading process is described by Mark L. Chambers (2004). CD & DVD Recording for Dummies (2nd ed.). John Wiley & Sons. p. 13. ISBN 0764559567.
General references 
- 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 00941413357
- Shannon, C. E., 2005 , "A Mathematical Theory of Communication," (corrected reprint), accessed Dec. 15, 2005. Orig. 1948, Bell System Technical Journal, vol. 27, pp. 379–423, 623-656.