thumb|right|In The Signal by [[William Powell Frith, a woman sends a signal by waving a white handkerchief.]]
A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields, including signal processing, information theory and biology.
In signal processing, a signal is a function that conveys information about a phenomenon.
The term analog signal usually refers to electrical signals; however, analog signals may use other mediums such as mechanical, pneumatic or hydraulic. An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage, current, or frequency of the signal may be varied to represent the information.
Any information may be conveyed by an analog signal; often, such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure. The physical variable is converted to an analog signal by a transducer. For example, in sound recording, fluctuations in air pressure (that is to say, sound) strike the diaphragm of a microphone, which induces corresponding electrical fluctuations. The voltage or the current is said to be an analog of the sound.
Digital signal
thumb|A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels.
A digital signal is a signal that is constructed from a discrete set of waveforms of a physical quantity so as to represent a sequence of discrete values. A logic signal is a digital signal with only two possible values, and describes an arbitrary bit stream. Other types of digital signals can represent three-valued logic or higher-valued logics.
Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity. The physical quantity may be a variable electric current or voltage, the intensity, phase or polarization of an optical or other electromagnetic field, acoustic pressure, the magnetization of a magnetic storage media, etc. Digital signals are present in all digital electronics, notably computing equipment and data transmission.
With digital signals, system noise, provided it is not too great, will not affect system operation, whereas noise always degrades the operation of analog signals to some degree.
Digital signals often arise via sampling of analog 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 and represent each reading with a fixed number of bits. The resulting stream of numbers is stored as digital data on a discrete-time and quantized-amplitude signal. Computers and other digital devices are restricted to discrete time.
Energy and power
According to the strengths of signals, practical signals can be classified into two categories: energy signals and power signals.
Energy signals: Those signals' energy are equal to a finite positive value, but their average powers are 0;
<math>0 < E = \int_{-\infty }^{\infty } s^2(t)dt < \infty </math>
Power signals: Those signals' average power are equal to a finite positive value, but their energy are infinite.
<math>P = \lim_{T\rightarrow \infty} \frac{1}{T} \int_{-T/2 }^{T/2} s^2(t)dt </math>
Deterministic and random
Deterministic signals are those whose values at any time are predictable and can be calculated by a mathematical equation.
Random signals are signals that take on random values at any given time instant and must be modeled stochastically.
Even and odd
An even signal satisfies the condition <math>x(t) = x(-t)</math>
or equivalently if the following equation holds for all <math>t</math> and <math>-t</math> in the domain of <math>x</math>:
:<math>x(t) - x(-t) = 0.</math>
An odd signal satisfies the condition <math>x(t) = - x(-t)</math>
or equivalently if the following equation holds for all <math>t</math> and <math>-t</math> in the domain of <math>x</math>:
:<math>x(t) + x(-t) = 0.</math>
Periodic
A signal is said to be periodic if it satisfies the condition:
<math>x(t) = x(t + T)\quad \forall t \in [t_0 , t_{max}]</math> or <math>x(n) = x(n + N)\quad \forall n \in [n_0 , n_{max}]</math>
Where:
<math>T</math> = fundamental time period,
<math>1/T = f </math>= fundamental frequency.
The same can be applied to <math>N</math>. A periodic signal will repeat for every period.
Time discretization
right|thumb|Discrete-time signal created from a continuous signal by [[Sampling (signal processing)|sampling]]
Signals can be classified as continuous or discrete time. In the mathematical abstraction, the domain of a continuous-time 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 other subsets of real numbers). What these integers represent depends on the nature of the signal; most often, it is time.
A continuous-time signal is any function which is defined at every time t in an interval, most commonly an infinite interval. 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.
Amplitude quantization
If a signal is to be represented as a sequence of digital data, it is impossible to maintain exact precision – each number in the sequence must have a finite number of digits. As a result, the values of such a signal must be quantized into a finite set for practical representation. Quantization is the process of converting a continuous analog audio signal to a digital signal with discrete numerical values of integers.
Examples
Naturally occurring signals can be converted to electronic signals by various sensors. Examples include:
- Motion. The motion of an object can be considered to be a signal and can be monitored by various sensors to provide electrical signals.
The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, frequency, s and z. Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous-time signals (t), one might transform from the time domain to a frequency or s domain; or from discrete time (n) to frequency or z domains. Systems can also be transformed between these domains, like signals, with continuous to s and discrete to z.
Signals and systems is a subset of the field of mathematical modeling. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with dynamical systems tools, including differential equations, and recently, Lagrangians. Students are expected to understand the modeling tools as well as the mathematics, physics, circuit analysis, and transformations between the 8 domains.
Because mechanical engineering (ME) topics like friction, dampening etc. have very close analogies in signal science (inductance, resistance, voltage, etc.), many of the tools originally used in ME transformations (Laplace and Fourier transforms, Lagrangians, sampling theory, probability, difference equations, etc.) have now been applied to signals, circuits, systems and their components, analysis and design in EE. Dynamical systems that involve noise, filtering and other random or chaotic attractors and repellers have now placed stochastic sciences and statistics between the more deterministic discrete and continuous functions in the field. (Deterministic, as used here, means signals that are completely determined as functions of time).
EE taxonomists are still not decided where signals and systems falls within the whole field of signal processing vs. circuit analysis and mathematical modeling, but the common link of the topics that are covered in the course of study has brightened boundaries with dozens of books, journals, etc. called "Signals and Systems", and used as text and test prep for the EE, as well as, recently, computer engineering exams.
Gallery
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Signalman sends semaphore message from Pearl Harbor Control Tower c1960.jpg|A signalman sends a semaphore message from a Pearl Harbor Control Tower, .
Finnish distant signal displaying Expect Stop.jpg|A Finnish distant signal at the western approach to Muhos station is displaying Expect Stop.
Hailing a cab.jpg|A woman hailing a cab is sending a signal of availability to be picked up.
Signal flare during a rescue training mission.jpg|A flare is a common means to signal during dark or smoke-filled conditions.
</gallery>
See also
- Beacon
- Current loop – a signaling system in widespread use for process control
- Signal-to-noise ratio