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español eesti euskara فارسی suomi français gaeilge galego עברית हिन्दी magyar bahasa indonesia italiano 日本語 한국어 latina latviešu македонски nederlands norsk nynorsk norsk bokmål polski português русский srpskohrvatski српскохрватски simple english slovenščina shqip српски srpski sunda svenska kiswahili தமிழ் türkçe українська 粵語 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from fractional bandwidth range of usable frequencies this article is about the concept in signal theory and processing measured in hertz for use in computing and networking expressed in bits per second see bandwidth computing for other uses see bandwidth disambiguation 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 frequencies in a continuous band of frequencies it is typically measured in 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 bandwidth in hertz is a central concept in many fields including electronics information theory digital communications radio communications signal processing and spectroscopy and is one of the determinants of the capacity of a given communication channel a key characteristic of bandwidth is that any band of a given width can carry the same amount of information regardless of where that band is located in the frequency spectrum a for example a 3 khz band can carry a telephone conversation whether that band is at baseband as in a pots telephone line or modulated to some higher frequency however wide bandwidths are easier to obtain and process at higher frequencies because the fractional bandwidth is smaller overview edit 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 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 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 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 nyquist sampling rate bandwidth typically refers to baseband bandwidth in the context of nyquist symbol rate or shannon hartley channel capacity for communication systems it refers to passband bandwidth the 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 1 the essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal 2 x db bandwidth edit 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 2 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 3 db point that is the point where the spectral density is half its maximum value or the spectral amplitude in v displaystyle mathrm v or v h z displaystyle mathrm v sqrt hz is 70 7 of its maximum 3 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 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 db bandwidth of an electronic filter or communication channel is the part of the system s frequency response that lies within 3 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 db the 3 db bandwidth is the frequency range where attenuation is less than 3 db 3 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 db with a small variation for example within the 1 db interval in the stopband s the required attenuation in decibels is above a certain level for example 100 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 db bandwidth if the filter shows amplitude ripple within the passband the x db point refers to the point where the gain is x db below the nominal passband gain rather than x db below the maximum gain in signal processing and control theory the bandwidth is the frequency at which the closed loop system gain drops 3 db below peak in communication systems in calculations of the shannon hartley channel capacity bandwidth refers to the 3 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 b 2 w displaystyle b 2w where b displaystyle b 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 w displaystyle w 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 w displaystyle w to stay intact and the physical passband channel would require a passband filter of at least b displaystyle b to stay intact relative bandwidth edit see also antenna radio bandwidth and antenna measurement bandwidth the absolute bandwidth is not always the most appropriate or useful measure of bandwidth for instance in the field of antennas the difficulty of constructing an antenna to meet a specified absolute bandwidth is easier at a higher frequency than at a lower frequency for this reason bandwidth is often quoted relative to the frequency of operation which gives a better indication of the structure and sophistication needed for the circuit or device under consideration there are two different measures of relative bandwidth in common use fractional bandwidth b f displaystyle b_ mathrm f and ratio bandwidth b r displaystyle b_ mathrm r 4 in the following the absolute bandwidth is defined as follows b δ f f h f l displaystyle b delta f f_ mathrm h f_ mathrm l where f h displaystyle f_ mathrm h and f l displaystyle f_ mathrm l are the upper and lower frequency limits respectively of the band in question fractional bandwidth edit fractional bandwidth is defined as the absolute bandwidth divided by the center frequency f c displaystyle f_ mathrm c b f δ f f c displaystyle b_ mathrm f frac delta f f_ mathrm c the center frequency is usually defined as the arithmetic mean of the upper and lower frequencies so that f c f h f l 2 displaystyle f_ mathrm c frac f_ mathrm h f_ mathrm l 2 and b f 2 f h f l f h f l displaystyle b_ mathrm f frac 2 f_ mathrm h f_ mathrm l f_ mathrm h f_ mathrm l however the center frequency is sometimes defined as the geometric mean of the upper and lower frequencies f c f h f l displaystyle f_ mathrm c sqrt f_ mathrm h f_ mathrm l and b f f h f l f h f l displaystyle b_ mathrm f frac f_ mathrm h f_ mathrm l sqrt f_ mathrm h f_ mathrm l while the geometric mean is more rarely used than the arithmetic mean and the latter can be assumed if not stated explicitly the former is considered more mathematically rigorous it more properly reflects the logarithmic relationship of fractional bandwidth with increasing frequency 5 for narrowband applications there is only marginal difference between the two definitions the geometric mean version is inconsequentially larger for wideband applications they diverge substantially with the arithmetic mean version approaching 2 in the limit and the geometric mean version approaching infinity fractional bandwidth is sometimes expressed as a percentage of the center frequency percent bandwidth b displaystyle b b f 100 δ f f c displaystyle b_ mathrm f 100 frac delta f f_ mathrm c ratio bandwidth edit ratio bandwidth is defined as the ratio of the upper and lower limits of the band b r f h f l displaystyle b_ mathrm r frac f_ mathrm h f_ mathrm l ratio bandwidth may be notated as b r 1 displaystyle b_ mathrm r 1 the relationship between ratio bandwidth and fractional bandwidth is given by b f 2 b r 1 b r 1 displaystyle b_ mathrm f 2 frac b_ mathrm r 1 b_ mathrm r 1 and b r 2 b f 2 b f displaystyle b_ mathrm r frac 2 b_ mathrm f 2 b_ mathrm f percent bandwidth is a less meaningful measure in wideband applications a percent bandwidth of 100 corresponds to a ratio bandwidth of 3 1 all higher ratios up to infinity are compressed into the range 100 200 ratio bandwidth is often expressed in octaves i e as a frequency level for wideband applications an octave is a frequency ratio of 2 1 leading to this expression for the number of octaves log 2 b r displaystyle log _ 2 left b_ mathrm r right noise equivalent bandwidth edit setup for the measurement of the noise equivalent bandwidth b n displaystyle b_ n of the system with frequency response h f displaystyle h f further information spectral leakage noise bandwidth the noise equivalent bandwidth or equivalent noise bandwidth enbw of a system of frequency response h f displaystyle h f is the bandwidth of an ideal filter with rectangular frequency response centered on the system s central frequency that produces the same average power outgoing h f displaystyle h f when both systems are excited with a white noise source the value of the noise equivalent bandwidth depends on the ideal filter reference gain used typically this gain equals h f displaystyle h f at its center frequency 6 but it can also equal the peak value of h f displaystyle h f the noise equivalent bandwidth b n displaystyle b_ n can be calculated in the frequency domain using h f displaystyle h f or in the time domain by exploiting the parseval s theorem with the system impulse response h t displaystyle h t if h f displaystyle h f is a lowpass system with zero central frequency and the filter reference gain is referred to this frequency then b n h f 2 d f 2 h 0 2 h t 2 d t 2 h t d t 2 displaystyle b_ n frac int _ infty infty h f 2 df 2 h 0 2 frac int _ infty infty h t 2 dt 2 left int _ infty infty h t dt right 2 the same expression can be applied to bandpass systems by substituting the equivalent baseband frequency response for h f displaystyle h f the noise equivalent bandwidth is widely used to simplify the analysis of telecommunication systems in the presence of noise photonics edit in photonics the term bandwidth carries 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 power meter can operate the data rate e g in gbit s achieved in an optical communication system see bandwidth computing a related concept is the spectral linewidth of the radiation emitted by excited atoms see also edit look up bandwidth in wiktionary the free dictionary bandwidth extension broadband noise bandwidth rise time spectral efficiency spectral width notes edit the information capacity of a channel depends on noise level as well as bandwidth see shannon hartley theorem equal bandwidths can carry equal information only when subject to equal signal to noise ratios references edit jeffrey a nanzer microwave and millimeter wave remote sensing for security applications pp 268 269 artech house 2012 isbn 1608071723 sundararajan d 4 march 2009 a practical approach to signals and systems john wiley sons p 109 isbn 978 0 470 82354 5 van valkenburg m e 1974 network analysis 3rd ed prentice hall pp 383 384 isbn 0 13 611095 9 retrieved 2008 06 22 stutzman warren l theiele gary a 1998 antenna theory and design 2nd ed new york isbn 0 471 02590 9 cite book cs1 maint location missing publisher link hans g schantz the art and science of ultrawideband antennas p 75 artech house 2015 isbn 1608079562 jeruchim m c balaban p shanmugan k s 2000 simulation of communication systems modeling methodology and techniques 2nd ed kluwer academic isbn 0 306 46267 2 authority control databases gnd retrieved from https en wikipedia org w index php title bandwidth_ signal_processing oldid 1332745200 fractional_bandwidth categories signal processing telecommunication theory filter frequency response spectrum physical 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