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Encyclopedia > Bandwidth

In computer networking literature, digital bandwidth refers to data rate measured in bit/s, for example channel capacity (digital bandwidth capacity) or throughput (digital bandwidth consumption). The reason for this usage is that the channel capacity in bit/s is proportional to the analogue bandwidth in hertz according to Hartley's law. This article or section is in need of attention from an expert on the subject. ... In telecommunication, data signaling rate (DSR) is the aggregate rate at which data pass a point in the transmission path of a data transmission system. ... This article does not cite any references or sources. ... In communication networks, throughput is the amount of digital data per time unit that is delivered over a physical or logical link, or that is passing through a certain network node. ... In information theory, the Shannonâ€“Hartley theorem is an application of the noisy channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. ...

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. For the musical use of modulation, see modulation (music). ... This article or section does not adequately cite its references or sources. ... For the book by Sir Isaac Newton, see Opticks. ... A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ... Legend Î³ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultra high frequency VHF = Very high frequency HF = High...

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. Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ...

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. In mathematics, the support of a real-valued function f on a set X is sometimes defined as the subset of X on which f is nonzero. ... For other uses, see Decibel (disambiguation). ...

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). In information theory, the Shannonâ€“Hartley theorem is an application of the noisy channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. ...

## Analog systems

A graph of a filter's gain magnitude, illustrating the concept of -3 dB (or half-power) bandwidth, at a gain of 0.707. The frequency axis of this symbolic diagram can be linear or logarithmically scaled.

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 $approx -3$ dB, since $10 mathrm{log}_{10}(1/2) approx -3$ ; see Decibel). 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. Image File history File links Bandwidth. ... Image File history File links Bandwidth. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... An analog or analogue signal is any time continuous signal where some time varying feature of the signal is a representation of some other time varying quantity. ... This article is about the SI unit of frequency. ... In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ... For other uses, see Decibel (disambiguation). ...

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. Baseband is an adjective that describes signals and systems whose range of frequencies is measured from 0 to a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies starting at 0. ...

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 a lowpass filter with cutoff frequency of at least W to stay intact. Please refer to Real vs. ... Baseband is an adjective that describes signals and systems whose range of frequencies is measured from 0 to a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies starting at 0. ... A low-pass filter passes low frequencies fairly well, but attenuates high frequencies. ...

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. Television signal splitter consisting of a hi-pass filter (left) and a low-pass filter (right). ... The frequency axis of this symbolic diagram would be logarithmically scaled. ...

In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak. For control theory in psychology and sociology, see control theory (sociology). ... A Proportional-Integral-Derivative controller is a standard feedback loop component in industrial control applications. ...

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).

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

In telecommunication, data signaling rate (DSR) is the aggregate rate at which data pass a point in the transmission path of a data transmission system. ...

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 Bandwidth - Wikipedia, the free encyclopedia (856 words) Bandwidth is a measure of frequency range, measured in hertz, of a function of a frequency variable. Bandwidth is a central concept in many fields, including information theory, radio communications, signal processing, and spectroscopy. The bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at the center frequency of its peak.
 Bandwidth - encyclopedia article about Bandwidth. (2189 words) Bandwidth is closely related to the the capacity of a communications channel: the two are related by Shannon-Hartley theorem. In radio communications, bandwidth is the range of frequencies occupied by a modulated carrier wave, while in optics it is the width of a spectral line or spectral range. Hence a 66 MHz digital data bus with 32 separate data lines may properly be said to have a bandwidth of 66 MHz and a capacity of 2.1 Gbit/s — but it would not be surprising to hear such a bus described as a having a "bandwidth of 2.1 Gbit/s".
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