Bandwidth
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Bandwidth is a measure of frequency range and is typically measured in hertz. Bandwidth is a central concept in many fields, including information theory, radio communications, signal processing, and spectroscopy. Bandwidth is related to channel capacity for information transmission and often the two can be confused. In particular, in common usage "bandwidth" also refers to data (information) transmission rates when communicating over certain media or devices.
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[edit] Overview
Bandwidth is a key concept in many applications. In radio communications, for example, bandwidth is the range of frequencies occupied by a modulated carrier wave, whereas in optics it is the width of an individual spectral line or the entire spectral range.
There is no single universal precise definition of bandwidth, as it is vaguely understood to be a measure of how wide a function is in the frequency domain.
For different applications there are different precise definitions. For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero. This would correspond to the mathematical notion of the support of a function (i.e., the total "length" of values for which the function is nonzero). A less strict and more practically useful definition will refer to the frequencies where the frequency function is small. Small could mean less than 3 dB below (i.e., less than half of) the maximum value, or more rarely 10 dB, 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.
According to the Shannon–Hartley theorem, the data rate of reliable communication is directly proportional to the frequency range of the signal used for the communication. In this context, the word bandwidth can refer to either the data rate or the frequency range of the communication system (or both).
[edit] Analog systems
For analog signals, which can be mathematically viewed as functions of time, bandwidth BW or Δf is the width, measured in hertz, of the frequency range in which the signal's Fourier transform is nonzero. Because this range of non-zero amplitude may be very broad, this definition is often relaxed so that the bandwidth is defined as the range of frequencies where the signal's Fourier transform has a power above a certain amplitude threshold, commonly half the maximum value (half power 
-3 dB, since 
). Bandwidth of a signal is a measure of how rapidly its parameters (e.g. amplitude and phase) fluctuate with respect to time. Hence, the greater the bandwidth, the faster the variation in the signal parameters may be. The word bandwidth applies to signals as described above, but it could also apply to systems. In the latter case, to say that a system has a certain bandwidth means that the system can process signals of that bandwidth.
A baseband bandwidth is a specification of only the highest frequency limit of a signal. A non-baseband bandwidth is a difference between highest and lowest frequencies.
As an example, the (non-baseband) 3-dB bandwidth of the function depicted in the figure is 
, whereas other definitions of bandwidth would yield a different answer.
A commonly used quantity is fractional bandwidth. This is the bandwidth of a device divided by its center frequency. E.g., a device that has a bandwidth of 2 MHz with center frequency 10 MHz will have a fractional bandwidth of 2/10, or 20%.
The fact that real baseband systems have 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 B = 2W, where B is the total bandwidth, and W is the positive bandwidth. For instance, this signal would require a lowpass filter with cutoff frequency of at least W to stay intact.
The 3-dB bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at its peak, which is typically at or near its center frequency.
In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak.
In basic electric circuit theory when studying Band-pass and Band-reject filters the bandwidth represents the distance between the two points in the frequency domain where the signal is 
of the maximum signal amplitude (half power).
In photonics, the term bandwidth occurs in 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 powermeter) can operate
- the data rate (e.g., in Gbit/s) achieved in an optical communication system
[edit] Digital systems
When used to discuss digital communication, the meaning of "bandwidth" is clouded by metaphorical use. Technicians sometimes use it as slang for baud rate, the rate at which symbols may be transmitted through the system. It is also used more colloquially to describe channel capacity, the rate at which bits may be transmitted through the system (see Shannon Limit). Hence, a digital data bus with a bit rate of 66 Mbps on each of 32 separate data lines may properly be said to have a bandwidth of 33 MHz and a capacity of 2.1 Gbit/s — but it would not be surprising to hear such a bus described as having a "bandwidth of 2.1 Gbit/s." Similar confusion exists for voiceband modems, where each symbol carries multiple bits of information so that a modem may transmit 56 kbit/s of information over a phone line with a bandwidth of only 4 kHz and a symbol rate of 8 Kbaud. A related metric which is used to measure the aggregated bandwidth of a whole network is bisection bandwidth.
Bandwidth is also used in the sense of commodity, referring to something limited or something costing money. Thus, communication costs bandwidth, and improper use of someone else's bandwidth may be called bandwidth theft.
In discrete time systems and digital signal processing, bandwidth is related to sampling rate according to the Nyquist-Shannon sampling theorem.
When Additive white Gaussian noise is present in a digital communication channel, the Shannon–Hartley theorem gives the relationship between the channel's bandwidth, the channel's capacity, and the Signal-to-noise ratio (SNR) ratio of the system.
[edit] Meaning of bandwidth in web hosting
In website hosting, the term "bandwidth" is often incorrectly used to describe the amount of data that can be transferred to or from the website or server, measured in bytes transferred over a prescribed period of time. This can be more accurately described as "Monthly Data Transfer".
Web hosting companies often quote a monthly bandwidth limit for a website, for example 500 gigabytes per month. If visitors to the website download a total greater than 500 gigabytes in one month, the bandwidth limit will have been exceeded.
[edit] See also
- Narrowband
- Broadband
- Modulation
- Bandwidth extension
- Shannon–Hartley theorem
- List of device bandwidths
- Comparison of latency and throughput
- Bandwidth theft
- Bandwidth cap
- Throughput
- Measuring network throughput
- Bitrate
- Q-factor
- Bandwidth test
- Goodput
