Varying physical quantity that conveys information
Signal
refers to 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.
[1]
Any quantity that can vary over space or time can be used as a signal to share messages between observers.
[2]
The
IEEE Transactions on Signal Processing
includes
audio
,
video
, speech,
image
,
sonar
, and
radar
as examples of signals.
[3]
A signal may also be defined as
any
observable change in a quantity over space or time (a
time series
), even if it does not carry information.
[a]
In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with
cell signaling
.
Signaling theory
, in
evolutionary biology
, proposes that a substantial driver for
evolution
is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically 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.
[1]
Another important property of a signal is its
entropy
or
information content
.
Information theory
serves as the formal study of signals and their content. The information of a signal is often accompanied by
noise
, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (
crosstalk
). The reduction of noise is covered in part under the heading of
signal integrity
. The separation of desired signals from background noise is the field of
signal recovery
,
[5]
one branch of which is
estimation theory
, a probabilistic approach to suppressing random disturbances.
Engineering disciplines such as electrical engineering have advanced 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:
electronic engineering
and
computer engineering
developed to specialize in the design and analysis of systems that manipulate physical signals, while
design engineering
developed to address the functional design of signals in
user?machine interfaces
.
Definitions
[
edit
]
Definitions specific to sub-fields are common:
- In
electronics
and
telecommunications
,
signal
refers to any time-varying
voltage
,
current
, or
electromagnetic wave
that carries information.
- In
signal processing
, signals are analog and digital representations of analog physical quantities.
- 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
to create a signal, which is carried to a
receiver
by the communication 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 signal. The signal is transmitted to the receiving telephone by wires; at the receiver it is reconverted into sounds.
- In telephone networks,
signaling
, for example
common-channel signaling
, refers to phone number and other digital control information rather than the actual voice signal.
Classification
[
edit
]
Signals can be categorized in various ways. The most common
[
verification needed
]
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
.
A second important distinction is between discrete-valued and continuous-valued. Particularly in
digital signal processing
, a
digital signal
may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In
digital electronics
, digital signals are the continuous-time waveform signals in a digital system, representing a bit-stream.
Signals may also be categorized by their spatial distributions as either point source signals (PSSs) or distributed source signals (DSSs).
[2]
In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into
analog signals
and
digital signals
; according to the determinacy of signals, classified into deterministic signals and random signals; according to the
strength of signals
, classified into energy signals and power signals.
Analog and digital signals
[
edit
]
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
quantized
, while analog signals are continuous.
Analog signal
[
edit
]
An analog signal is any
continuous signal
for which the time-varying feature of the signal is a representation of some other time varying quantity, i.e.,
analogous
to another time varying signal. For example, in an analog
audio signal
, the instantaneous
voltage
of the signal varies continuously with the
sound pressure
. It differs from a
digital signal
, in which the continuous quantity is a representation of a sequence of
discrete values
which can only take on one of a finite number of values.
[6]
[7]
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
[
edit
]
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.
[8]
[9]
[10]
A
logic signal
is a digital signal with only two possible values,
[11]
[12]
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.
[13]
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
[
edit
]
According to the strengths of signals, practical signals can be classified into two categories: energy signals and power signals.
[14]
Energy signals: Those signals'
energy
are equal to a finite positive value, but their average powers are 0;
Power signals: Those signals' average
power
are equal to a finite
positive
value, but their energy are
infinite
.
Deterministic and random
[
edit
]
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
.
[15]
Even and odd
[
edit
]
is an example of an even signal.
is an example of an odd signal.
An
even signal
satisfies the condition
or equivalently if the following equation holds for all
and
in the domain of
:
An odd signal satisfies the condition
or equivalently if the following equation holds for all
and
in the domain of
:
Periodic
[
edit
]
A signal is said to be
periodic
if it satisfies the condition:
or
Where:
= fundamental time
period
,
= fundamental
frequency
.
A periodic signal will repeat for every period.
Time discretization
[
edit
]
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
[
edit
]
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 of signals
[
edit
]
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.
[16]
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
.
[17]
- 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 possibly three space coordinates indicating the direction of travel. A sound signal is converted to an electrical signal by a
microphone
, generating a
voltage
signal as an analog of the sound signal. 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 Hz
; since CDs are recorded in
stereo
, each sample contains data for a left and right channel, which may be considered to be a 2-vector signal. The CD encoding is converted to an electrical signal by reading the information with a
laser
, converting the sound signal to an optical signal.
[18]
- 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 emitted or reflected
light
, an electromagnetic 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
digital image
. Color images are typically represented as a combination of monochrome images in three
primary colors
.
- Videos
. A video signal is a sequence of images. A point in a video is identified by its two-dimensional position in the image 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
electrophysiology
techniques.
- The output of a
thermocouple
, which conveys temperature information.
[1]
- The output of a
pH meter
which conveys acidity information.
[1]
Signal processing
[
edit
]
Signal processing is the manipulation of signals. 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 its original form to a
waveform
expressed as a
current
or a
voltage
, or
electromagnetic radiation
, 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
filters
, and can be transmitted to a remote location by a
transmitter
and received using
radio receivers
.
Signals and systems
[
edit
]
In
electrical engineering
(EE) programs, signals are covered in a class and field of study known as
signals and systems
. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous
linear algebra
and
differential equation
classes they have taken.
[19]
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 also can 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.
[20]
Gallery
[
edit
]
See also
[
edit
]
Notes
[
edit
]
- ^
Some authors do not emphasize the role of information in the definition of a signal.
[4]
References
[
edit
]
- ^
a
b
c
d
Roland Priemer (1991).
Introductory Signal Processing
. World Scientific. p. 1.
ISBN
978-9971509194
.
Archived
from the original on 2013-06-02.
A signal is a function that conveys information about the behavior of a system or attributes of some phenomenon.
- ^
a
b
Chakravorty, Pragnan (2018). "What Is a Signal? [Lecture Notes]".
IEEE Signal Processing Magazine
.
35
(5): 175?177.
Bibcode
:
2018ISPM...35e.175C
.
doi
:
10.1109/MSP.2018.2832195
.
S2CID
52164353
.
Consequently, a signal, represented as a function of one or more variables, may be defined as an observable change in a quantifiable entity.
- ^
"Aims and scope"
.
IEEE Transactions on Signal Processing
.
IEEE
.
Archived
from the original on 2012-04-17.
- ^
Priyabrata Sinha (2009).
Speech processing in embedded systems
. Springer. p. 9.
ISBN
978-0387755809
.
Archived
from the original on 2013-06-02.
To put it very generally, a signal is any time-varying physical quantity.
- ^
T. H. Wilmshurst (1990).
Signal Recovery from Noise in Electronic Instrumentation
(2nd ed.). CRC Press. pp. 11
ff
.
ISBN
978-0750300582
.
Archived
from the original on 2015-03-19.
- ^
"Digital signals"
.
www.st-andrews.ac.uk
.
Archived
from the original on 2017-03-02
. Retrieved
2017-12-17
.
- ^
"Analog vs. Digital - learn.sparkfun.com"
.
learn.sparkfun.com
.
Archived
from the original on 2017-07-05
. Retrieved
2017-12-17
.
- ^
Robert K. Dueck (2005).
Digital Design with CPLD Applications and VHDL
. Thomson/Delmar Learning.
ISBN
1401840302
. Archived from
the original
on 2017-12-17.
A digital representation can have only specific discrete values
- ^
Proakis, John G.;
Manolakis, Dimitris G.
(2007-01-01).
Digital Signal Processing
. Pearson Prentice Hall.
ISBN
9780131873742
.
Archived
from the original on 2016-05-20.
- ^
Smillie, Grahame (1999-04-02).
Analogue and Digital Communication Techniques
. Elsevier.
ISBN
9780080527147
. Archived from
the original
on 2017-12-17.
A digital signal is a complex waveform and can be defined as a discrete waveform having a finite set of levels
- ^
"Digital Signal"
.
Archived
from the original on 2019-04-02
. Retrieved
2016-08-13
.
- ^
Paul Horowitz; Winfield Hill (2015).
The Art of Electronics
. Cambridge University Press.
ISBN
9780521809269
.
- ^
Vinod Kumar Khanna (2009).
Digital Signal Processing
. S. Chand. p. 3.
ISBN
9788121930956
.
A digital signal is a special form of discrete-time signal which is discrete in both time and amplitude, obtained by permitting each value (sample) of a discrete-time signal to acquire a finite set of values (quantization), assigning it a numerical symbol according to a code ... A digital signal is a sequence or list of numbers drawn from a finite set.
- ^
Sklar, Bernard, 1927? (2001).
Digital communications : fundamentals and applications
(2nd ed.). Upper Saddle River, N.J.: Prentice-Hall PTR.
ISBN
0130847887
.
OCLC
45823120
.
{{
cite book
}}
: CS1 maint: multiple names: authors list (
link
) CS1 maint: numeric names: authors list (
link
)
- ^
Ziemer, Rodger E. (2014-03-17).
Principles of communication : systems, modulation, and noise
. Tranter, William H. (Seventh ed.). Hoboken, New Jersey.
ISBN
9781118078914
.
OCLC
856647730
.
{{
cite book
}}
: CS1 maint: location missing publisher (
link
)
- ^
For an example from robotics, see
K Nishio & 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 (eds.).
Neural Information Processing: 18th International Conference, Iconip 2011, Shanghai, China, November 13?17, 2011
. Springer. pp. 506
ff
.
ISBN
978-3642249648
.
Archived
from the original on 2013-06-02.
- ^
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
978-3642154935
.
Archived
from the original on 2013-06-02.
- ^
The optical reading process is described by
Mark L. Chambers (2004).
CD & DVD Recording for Dummies
(2nd ed.). John Wiley & Sons. p. 13.
ISBN
978-0764559563
.
Archived
from the original on 2013-06-02.
- ^
David McMahon (2007).
Signals & Systems Demystified
. New York: McGraw Hill.
ISBN
978-0-07-147578-5
.
Archived
from the original on 2020-01-22
. Retrieved
2017-09-11
.
- ^
M.J. Roberts (2011).
Signals and Systems: Analysis Using Transform Methods & MATLAB
. New York: McGraw Hill.
ISBN
978-0073380681
.
Further reading
[
edit
]
- Hsu, P. H. (1995).
Schaum's Theory and Problems: Signals and Systems
. McGraw-Hill.
ISBN
0-07-030641-9
.
- Lathi, B.P. (1998).
Signal Processing & Linear Systems
. Berkeley-Cambridge Press.
ISBN
0-941413-35-7
.