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Bandwidth (signal processing)

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Baseband bandwidth. Here the bandwidth equals the upper frequency.

Bandwidth is the difference between the upper and lower frequencies in a contiguous set of frequencies. It is typically measured in hertz, and may sometimes refer to passband bandwidth, sometimes to baseband bandwidth, depending on context. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, an electronic filter, a communication channel, or a signal spectrum. In case of a low-pass filter or baseband signal, the bandwidth is equal to its upper cutoff frequency. The term ...view middle of the document...

Contents * 1 Overview * 2 X-dB bandwidth * 3 Antenna systems * 4 Photonics * 5 See also * 6 References |

[edit] Overview

Bandwidth is a key concept in many telephony applications. In radio communications, for example, bandwidth is the frequency range occupied by a modulated carrier wave, whereas in optics it is the width of an individual spectral 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 broadcast license holders 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., power output < 1/2 or voltage output < 0.707 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.

Bandwidth typically refers to baseband bandwidth in the context of, for example, sampling theorem and Nyquist sampling rate, while it refers to passband bandwidth in the context of Nyquist symbol rate or Shannon-Hartley channel capacity for communication systems.

[edit] X-dB bandwidth

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

In some contexts, the signal bandwidth in hertz refers to the frequency range in which the signal's spectral density is nonzero or above a small threshold value. That definition is used in calculations of the lowest sampling rate that will satisfy the sampling theorem. Because this range of non-zero amplitude may be very broad or infinite, this definition is typically relaxed so that the bandwidth is defined as the range of frequencies in which the signal's spectral density is above a certain threshold relative to its maximum. Most commonly, bandwidth refers to the 3-dB bandwidth, that is, the frequency range within which the spectral density (in W/Hz or V2/Hz) is above half its maximum value (or the spectral amplitude, in V or V/Hz, is more than 70.7% of its maximum); that is, above −3 dB relative to the peak.[1]

The word bandwidth applies to signals as described above, but...

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