Bandwidth (signal processing): Difference between revisions
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imported>Johnuniq m Reverted edit by 97.118.204.130 (talk) to last version by Graham87 |
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[[Image:Baseband.svg|right|300px|thumb|Amplitude (a) vs. frequency (f) graph illustrating [[baseband]] bandwidth. Here the bandwidth equals the upper frequency.]] | [[Image:Baseband.svg|right|300px|thumb|Amplitude (a) vs. frequency (f) graph illustrating [[baseband]] bandwidth. Here the bandwidth equals the upper frequency.]] | ||
'''Bandwidth''' is the difference between the upper and lower [[ | '''Bandwidth''' is the difference between the upper and lower [[frequencies]] in a continuous [[Frequency band|band of frequencies]]. It is typically measured in [[unit of measurement|unit]] of [[hertz]] (symbol Hz). | ||
It may refer more specifically to two subcategories: ''[[Passband]] bandwidth'' is the difference between the upper and lower [[cutoff frequencies]] of, for example, a [[band-pass filter]], a [[communication channel]], or a [[signal spectrum]]. ''[[Baseband]] bandwidth'' is equal to the upper cutoff frequency of a [[low-pass filter]] or baseband signal, which includes a zero frequency. | It may refer more specifically to two subcategories: ''[[Passband]] bandwidth'' is the difference between the upper and lower [[cutoff frequencies]] of, for example, a [[band-pass filter]], a [[communication channel]], or a [[signal spectrum]]. ''[[Baseband]] bandwidth'' is equal to the upper cutoff frequency of a [[low-pass filter]] or baseband signal, which includes a zero frequency. | ||
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== Overview == | == Overview == | ||
Bandwidth is a key concept in many [[telecommunications]] applications. In [[radio]] communications, for example, bandwidth is the frequency range occupied by a modulated [[carrier signal]]. An [[FM radio]] receiver's [[tuner (radio)|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 [[broadcast license]] holders so that their [[signal | Bandwidth is a key concept in many [[telecommunications]] applications. In [[radio]] communications, for example, bandwidth is the frequency range occupied by a modulated [[carrier signal]]. An [[FM radio]] receiver's [[tuner (radio)|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 [[broadcast license]] holders so that their [[signal]]s do not mutually interfere. In this context, bandwidth is also known as [[channel spacing]]. | ||
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]], degradation could, for example, mean more than 3 [[decibel|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. | 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]], degradation could, for example, mean more than 3 [[decibel|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]] and [[ | In the context of, for example, the [[sampling theorem]] and [[Nyquist sampling rate]], bandwidth typically refers to [[baseband]] bandwidth. In the context of [[Nyquist rate|Nyquist symbol rate]] or [[Shannon-Hartley]] [[channel capacity]] for communication systems it refers to [[passband]] bandwidth. | ||
The '''{{vanchor|Rayleigh bandwidth}}''' 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.<ref>Jeffrey A. Nanzer, ''Microwave and Millimeter-wave Remote Sensing for Security Applications'', pp. 268-269, Artech House, 2012 {{ISBN|1608071723}}.</ref> | The '''{{vanchor|Rayleigh bandwidth}}''' 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.<ref>Jeffrey A. Nanzer, ''Microwave and Millimeter-wave Remote Sensing for Security Applications'', pp. 268-269, Artech House, 2012 {{ISBN|1608071723}}.</ref> | ||
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[[Image:Bandwidth 2.svg|right|300px|thumb|The magnitude response of a [[band-pass filter]] illustrating the concept of −3 dB bandwidth at a gain of approximately 0.707]] | [[Image:Bandwidth 2.svg|right|300px|thumb|The magnitude response of a [[band-pass filter]] illustrating the concept of −3 dB bandwidth at a gain of approximately 0.707]] | ||
In some contexts, the signal bandwidth in [[hertz]] refers to the frequency range in which the signal's [[spectral density]] (in W/Hz or V<sup>2</sup>/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 {{no wrap|[[3 dB point]]}}, that is the point where the spectral density is half its maximum value (or the spectral amplitude, in <math>\mathrm{V}</math> or <math>\mathrm{V/\sqrt{Hz}}</math>, is 70.7% of its maximum).<ref> | In some contexts, the signal bandwidth in [[hertz]] refers to the frequency range in which the signal's [[spectral density]] (in W/Hz or V<sup>2</sup>/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 {{no wrap|[[Cutoff frequency|3 dB point]]}}, that is the point where the spectral density is half its maximum value (or the spectral amplitude, in <math>\mathrm{V}</math> or <math>\mathrm{V/\sqrt{Hz}}</math>, is 70.7% of its maximum).<ref> | ||
{{cite book | {{cite book | ||
|title=Network Analysis | |title=Network Analysis | ||