- Bandwidth (signal processing)
**Bandwidth**is the difference between the upper and lowercutoff frequencies of, for example, a filter, acommunication channel , or asignal spectrum , and is typically measured inhertz . In case of abaseband channel or signal, the bandwidth is equal to its upper cutoff frequency. Bandwidth in hertz is a central concept in many fields, includingelectronics ,information theory ,radio communication s,signal processing , andspectroscopy .In

computer networking and other digital fields, the term "bandwidth" often refers to a data rate measured in bits per second, for example networkthroughput . The reason is that according toHartley's law , the digital data rate limit (orchannel capacity ) of a physical communication link is related to its bandwidth in hertz, sometimes denoted "analog bandwidth". For "bandwidth" as a computing term, less ambiguous terms arebit rate ,throughput ,goodput or channel capacity.**Overview**Bandwidth is a key concept in many

telephony applications. Inradio communications, for example, bandwidth is the range of frequencies occupied by amodulated carrier wave , whereas inoptics it is the width of an individualspectral line or the entire spectral range.In many signal processing contexts, bandwidth is a valuable and limited resource. For example, an FM radio receiver's tuner spans a limited range of frequencies. A government agency (such as the

Federal Communications Commission in the United States) may apportion the regionally available bandwidth to licensed broadcasters so that their signals do not mutually interfere. Each transmitter owns a slice of bandwidth, a valuable (if intangible) commodity.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 below, 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.**Analog systems**For

analog signals , which can be mathematically viewed as functions of time,**bandwidth**BW or $Delta\; f$ is the width, measured inhertz , of the frequency range in which the signal'sFourier 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, or −3 dB. [*cite book*] 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 wordbandwidth applies to signals as described above, but it could also apply to "systems", for example

title=Network Analysis

edition=3rd edition

last=Van Valkenburg

first=M. E.

pages=pp. 383-384

isbn=0-13-611095-9

url=http://www.amazon.com/Network-Analysis-Mac-Van-Valkenburg/dp/0136110959

accessdate=2008-06-22filter s orcommunication channel s. To say that a system has a certain bandwidth means that the system can process signals of that bandwidth.A

baseband bandwidth is synonymous to the upper cutoff frequency, i.e. 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 $Delta\; f\; =\; f\_2\; -\; f\_1\; ,$, 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 alowpass 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 itscenter frequency .In signal processing and

control theory the bandwidth is the frequency at which theclosed-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 $frac\{1\}\{sqrt\{2$ of the maximum signal amplitude (half power).

**Photonics**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

*thedata rate (e.g., in Gbit/s) achieved in an optical communication system; seebandwidth (computing) .A related concept is the

spectral linewidth of the radiation emitted by excited atoms.**ee also*** (Wiktionary entry)

*Bandwidth efficiency

*Bandwidth extension

*Narrowband

*Modulation

*Q-factor

*Shannon–Hartley theorem

*Wideband **References**

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