Editing Bandwidth (signal processing) (section)

== ''x'' dB bandwidth ==

[[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>
{{cite book
|title=Network Analysis
|edition=3rd
|last=Van Valkenburg
|first=M. E.
|year=1974
|pages=[https://archive.org/details/networkanalysis00vanv/page/383 383–384]
|publisher=Prentice-Hall
|isbn=0-13-611095-9
|url=https://archive.org/details/networkanalysis00vanv/page/383
|access-date=2008-06-22
}}</ref> This figure, with a lower threshold value, can be used in calculations of the lowest sampling rate that will satisfy the [[sampling theorem]].  

The bandwidth is also used to denote '''system bandwidth''', for example in [[Electronic filter|filter]] or [[communication channel]] systems. To say that a system has a certain bandwidth means that the system can process signals with that range of frequencies, or that the system reduces the bandwidth of a white noise input to that bandwidth.

The 3&nbsp;dB bandwidth of an [[electronic filter]] or communication channel is the part of the system's frequency response that lies within 3&nbsp;dB of the response at its peak, which, in the passband filter case, is typically at or near its [[center frequency]], and in the low-pass filter is at or near its [[cutoff frequency]]. If the maximum gain is 0&nbsp;dB, the 3&nbsp;dB bandwidth is the frequency range where attenuation is less than 3&nbsp;dB. 3&nbsp;dB attenuation is also where power is half its maximum. This same ''half-power gain'' convention is also used in [[spectral width]], and more generally for the extent of functions as [[full width at half maximum]] (FWHM).

In [[electronic filter]] design, a filter specification may require that within the filter [[passband]], the gain is nominally 0&nbsp;dB with a small variation, for example within the ±1&nbsp;dB interval. In the [[stopband]](s), the required attenuation in decibels is above a certain level, for example >100&nbsp;dB. In a [[transition band]] the gain is not specified. In this case, the filter bandwidth corresponds to the passband width, which in this example is the 1&nbsp;dB-bandwidth. If the filter shows amplitude ripple within the passband, the ''x''&nbsp;dB point refers to the point where the gain is ''x''&nbsp;dB below the nominal passband gain rather than ''x''&nbsp;dB below the maximum gain.

In signal processing and [[control theory]] the bandwidth is the frequency at which the [[Closed-loop transfer function|closed-loop system gain]] drops 3&nbsp;dB below peak.

In communication systems, in calculations of the [[Shannon–Hartley]] [[channel capacity]], bandwidth refers to the 3&nbsp;dB-bandwidth. In calculations of the maximum [[symbol rate]], the [[Nyquist sampling rate]], and maximum bit rate according to the [[Hartley's law]], the bandwidth refers to the frequency range within which the gain is non-zero.

The fact that in equivalent [[baseband]] models of communication systems, the signal spectrum consists of 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 <math>B = 2W</math>, where <math>B</math> is the total bandwidth (i.e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel), and <math>W</math> is the positive bandwidth (the baseband bandwidth of the equivalent channel model).  For instance, the baseband model of the signal would require a [[low-pass filter]] with cutoff frequency of at least <math>W</math> to stay intact, and the physical passband channel would require a passband filter of at least <math>B</math> to stay intact.