Bandwidth is the difference between the upper and lower
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
in a continuous
band of frequencies. It is typically measured in
hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
, and depending on context, may specifically refer to ''
passband
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
bandwidth'' or ''
baseband
In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable into a ...
bandwidth''. Passband bandwidth is the difference between the upper and lower
cutoff frequencies
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather tha ...
of, for example, a
band-pass filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.
Description
In electronics and signal processing, a filter is usually a two-por ...
, a
communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
, or a
signal spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discre ...
. Baseband bandwidth applies to a
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...
or baseband signal; the bandwidth is equal to its upper cutoff frequency.
Bandwidth in hertz is a central concept in many fields, including
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
,
information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
,
digital communication
Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
s,
radio communication
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
s,
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...
, and
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
and is one of the determinants of the capacity of a given
communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
.
A key characteristic of bandwidth is that any band of a given width can carry the same amount of
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
, regardless of where that band is located in the
frequency spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
. For example, a 3 kHz band can carry a telephone conversation whether that band is at baseband (as in a
POTS telephone line) or
modulated
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
to some higher frequency. However, wide bandwidths are easier to obtain and
process
A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic.
Things called a process include:
Business and management
*Business process, activities that produce a specific se ...
at higher frequencies because the is smaller.
Overview
Bandwidth is a key concept in many
telecommunication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
s applications. In
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
communications, for example, bandwidth is the frequency range occupied by a modulated
carrier signal
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
. An
FM radio
FM broadcasting is a method of radio broadcasting using frequency modulation (FM). Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to provide high fidelity sound over broadcast radio. FM broadcasting is cap ...
receiver's
tuner spans a limited range of frequencies. A government agency (such as the
Federal Communications Commission
The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdiction ...
in the United States) may apportion the regionally available bandwidth to
broadcast license
A broadcast license is a type of spectrum license granting the licensee permission to use a portion of the radio frequency spectrum in a given geographical area for broadcasting purposes. The licenses generally include restrictions, which vary ...
holders so that their
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
do not mutually interfere. In this context, bandwidth is also known as
channel spacing Channel spacing, also known as bandwidth, is a term used in radio frequency planning. It describes the frequency difference between adjacent allocations in a frequency plan. Channels for mediumwave
Medium wave (MW) is the part of the medium f ...
.
For other applications, there are other definitions. One definition of bandwidth, for a system, could be the range of frequencies over which the system produces a specified level of performance. A less strict and more practically useful definition will refer to the frequencies beyond which performance is degraded. In the case of
frequency response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of sy ...
, degradation could, for example, mean more than 3
dB below the maximum value or it could mean below a certain absolute value. As with any definition of the ''width'' of a function, many definitions are suitable for different purposes.
In the context of, for example, the
sampling theorem
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
* Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a sound recording in ano ...
and
Nyquist sampling rate, bandwidth typically refers to
baseband
In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable into a ...
bandwidth. In the context of
Nyquist symbol rate or
Shannon-Hartley channel capacity for communication systems it refers to
passband
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
bandwidth.
The of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a Rayleigh bandwidth of one megahertz.
The is defined as the portion of a
signal spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discre ...
in the frequency domain which contains most of the energy of the signal.
''x'' dB bandwidth
In some contexts, the signal bandwidth in
hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
refers to the frequency range in which the signal's
spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, o ...
(in W/Hz or V
2/Hz) is nonzero or above a small threshold value. The threshold value is often defined relative to the maximum value, and is most commonly the , that is the point where the spectral density is half its maximum value (or the spectral amplitude, in
or
, is 70.7% of its maximum). This figure, with a lower threshold value, can be used in calculations of the lowest sampling rate that will satisfy the
sampling theorem
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
* Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a sound recording in ano ...
.
The bandwidth is also used to denote system bandwidth, for example in
filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
or
communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
systems. To say that a system has a certain bandwidth means that the system can process signals with that range of frequencies, or that the system reduces the bandwidth of a white noise input to that bandwidth.
The 3 dB bandwidth of an
electronic filter
Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
or communication channel is the part of the system's frequency response that lies within 3 dB of the response at its peak, which, in the passband filter case, is typically at or near its
center frequency
In electrical engineering and telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies. It is usually defined as either the arithmetic mean or the geometr ...
, and in the low-pass filter is at or near its
cutoff frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather than ...
. If the maximum gain is 0 dB, the 3 dB bandwidth is the frequency range where attenuation is less than 3 dB. 3 dB attenuation is also where power is half its maximum. This same ''half-power gain'' convention is also used in
spectral width In telecommunications, spectral width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value.
In optical communicat ...
, and more generally for the extent of functions as
full width at half maximum
In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve mea ...
(FWHM).
In
electronic filter
Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
design, a filter specification may require that within the filter
passband
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
, the gain is nominally 0 dB with a small variation, for example within the ±1 dB interval. In the
stopband
A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on applic ...
(s), the required attenuation in decibels is above a certain level, for example >100 dB. In a
transition band The transition band, also called the skirt, is a range of frequencies that allows a transition between a passband and a stopband of a signal processing filter. The transition band is defined by a passband and a stopband cutoff frequency or corner f ...
the gain is not specified. In this case, the filter bandwidth corresponds to the passband width, which in this example is the 1 dB-bandwidth. If the filter shows amplitude ripple within the passband, the ''x'' dB point refers to the point where the gain is ''x'' dB below the nominal passband gain rather than ''x'' dB below the maximum gain.
In signal processing and
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
the bandwidth is the frequency at which the
closed-loop system gain drops 3 dB below peak.
In communication systems, in calculations of the
Shannon–Hartley channel capacity, bandwidth refers to the 3 dB-bandwidth. In calculations of the maximum
symbol rate
In a digitally modulated signal or a line code, symbol rate, modulation rate or baud rate is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in ''b ...
, the
Nyquist sampling rate, and maximum bit rate according to the
Hartley's law
Hartley's is a brand of marmalades, jams and jellies, originally from the United Kingdom, which is manufactured at Histon, Cambridgeshire. The brand was formerly owned by Premier Foods, until it was sold along with the factory in Histon to Hain C ...
, the bandwidth refers to the frequency range within which the gain is non-zero.
The fact that in equivalent
baseband
In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable into a ...
models of communication systems, the signal spectrum consists of both negative and positive frequencies, can lead to confusion about bandwidth since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as
, where
is the total bandwidth (i.e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel), and
is the positive bandwidth (the baseband bandwidth of the equivalent channel model). For instance, the baseband model of the signal would require a
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...
with cutoff frequency of at least
to stay intact, and the physical passband channel would require a passband filter of at least
to stay intact.
Relative bandwidth
The absolute bandwidth is not always the most appropriate or useful measure of bandwidth. For instance, in the field of
antennas
In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies a ...
the difficulty of constructing an antenna to meet a specified absolute bandwidth is easier at a higher frequency than at a lower frequency. For this reason, bandwidth is often quoted relative to the frequency of operation which gives a better indication of the structure and sophistication needed for the circuit or device under consideration.
There are two different measures of relative bandwidth in common use: ''fractional bandwidth'' (
) and ''ratio bandwidth'' (
). In the following, the absolute bandwidth is defined as follows,
where
and
are the upper and lower frequency limits respectively of the band in question.
Fractional bandwidth
Fractional bandwidth is defined as the absolute bandwidth divided by the center frequency (
),
The center frequency is usually defined as the
arithmetic mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...
of the upper and lower frequencies so that,
and
However, the center frequency is sometimes defined as the
geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
of the upper and lower frequencies,
and
While the geometric mean is more rarely used than the arithmetic mean (and the latter can be assumed if not stated explicitly) the former is considered more mathematically rigorous. It more properly reflects the logarithmic relationship of fractional bandwidth with increasing frequency.
[Hans G. Schantz, ''The Art and Science of Ultrawideband Antennas'', p. 75, Artech House, 2015 ] For
narrowband
Narrowband signals are signals that occupy a narrow range of frequencies or that have a small fractional bandwidth. In the audio spectrum, narrowband sounds are sounds that occupy a narrow range of frequencies. In telephony, narrowband is usua ...
applications, there is only marginal difference between the two definitions. The geometric mean version is inconsequentially larger. For
wideband
In communications, a system is wideband when the message bandwidth significantly exceeds the coherence bandwidth of the Channel (communications), channel. Some communication links have such a high Bit rate, data rate that they are forced to use a ...
applications they diverge substantially with the arithmetic mean version approaching 2 in the limit and the geometric mean version approaching infinity.
Fractional bandwidth is sometimes expressed as a percentage of the center frequency (percent bandwidth,
),
Ratio bandwidth
Ratio bandwidth is defined as the ratio of the upper and lower limits of the band,
Ratio bandwidth may be notated as
. The relationship between ratio bandwidth and fractional bandwidth is given by,
and
Percent bandwidth is a less meaningful measure in wideband applications. A percent bandwidth of 100% corresponds to a ratio bandwidth of 3:1. All higher ratios up to infinity are compressed into the range 100–200%.
Ratio bandwidth is often expressed in
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s for wideband applications. An octave is a frequency ratio of 2:1 leading to this expression for the number of octaves,
Photonics
In
photonics
Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. Though ...
, the term ''bandwidth'' carries a variety of meanings:
*the bandwidth of the output of some light source, e.g., an ASE source or a laser; the bandwidth of ultrashort optical pulses can be particularly large
*the width of the frequency range that can be transmitted by some element, e.g. an optical fiber
*the gain bandwidth of an optical amplifier
*the width of the range of some other phenomenon, e.g., a reflection, the phase matching of a nonlinear process, or some resonance
*the maximum modulation frequency (or range of modulation frequencies) of an optical modulator
*the range of frequencies in which some measurement apparatus (e.g., a power meter) can operate
*the
data rate (e.g., in Gbit/s) achieved in an optical communication system; see
bandwidth (computing)
In computing, bandwidth is the maximum rate of data transfer across a given path. Bandwidth may be characterized as network bandwidth, data bandwidth, or digital bandwidth.
This definition of ''bandwidth'' is in contrast to the field of signal p ...
.
A related concept is the
spectral linewidth
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
of the radiation emitted by excited atoms.
See also
*
Bandwidth extension
Bandwidth extension of signal is defined as the deliberate process of expanding the frequency range (bandwidth) of a signal in which it contains an appreciable and useful content, and/or the frequency range in which its effects are such. Its signif ...
*
Broadband
In telecommunications, broadband is wide bandwidth data transmission which transports multiple signals at a wide range of frequencies and Internet traffic types, that enables messages to be sent simultaneously, used in fast internet connections. ...
*
Noise bandwidth
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum. Any linear time-invariant operation on s(t) produces a new spectrum of the form H(f)•S(f), which chang ...
*
Rise time In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. These values may be expressed as ratiosSee for example , and . or, equivalen ...
*
Spectral efficiency
Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is ut ...
Notes
References
{{DEFAULTSORT:Bandwidth (Signal Processing)
Signal processing
Telecommunication theory
Filter frequency response