View source for DBFS

{{Short description|Unit of measurement for amplitude levels in digital systems}}
{{other|DBFS (disambiguation)}}
{{lowercase|title=dBFS}}
[[File:Clipping.svg|thumb|right|Clipping of a digital waveform. The red lines indicate full scale, and the waveform is shown before and after hard clipping (grey and black outlines respectively).]]
'''[[Decibel]]s relative to [[full scale]]''' ('''dBFS''' or '''dB FS''') is a unit of measurement for amplitude levels in digital systems, such as [[pulse-code modulation]] (PCM), which have a defined maximum peak level. The unit is similar to the units '''dBov'''  and '''decibels relative to overload''' ('''dBO''').<ref>
{{Citation
 | quote=In all cases the reference power level used for measurements will be the overload point of the converter in question, and figures will be quoted in dBO.
 | last1=M. Thurston | first1=A
 | last2=H. Pearce  | first2=T
 | last3=D. Higman  | first3=M
 | last4=Hawksford  | first4=Malcolm
 | title=Bandpass Sigma Delta A-D Conversion
 | date=1993-01-01
 | url=https://www.researchgate.net/publication/312797930
 | pages=259–281 | publisher=Springer | isbn=9781441951311
 | access-date=2018-07-27
}}</ref>

The level of 0{{nnbsp}}dBFS is assigned to the maximum possible digital level.<ref name='jp'>
{{cite web
  | last =Price
  | first =Jim
  | title =Understanding dB
  | work =Professional Audio
  | url =http://www.jimprice.com/prosound/db.htm
  | access-date = 2007-03-13
}}</ref> For example, a signal that reaches 50% of the maximum level has a level of −6{{nnbsp}}dBFS, which is 6{{nnbsp}}dB below full scale. Conventions differ for [[root mean square]] (RMS) measurements, but all peak measurements smaller than the maximum are negative levels.

A digital signal that does not contain any samples at 0{{nnbsp}}dBFS can still [[Clipping (audio)|clip]] when converted to analog form due to the [[signal reconstruction]] process interpolating between samples.<ref>{{Cite web|url=https://service.tcgroup.tc/media/Level_paper_AES109%281%29.pdf|title=0dBFS+ Levels in Digital Mastering|last1=Nielsen|first1=Søren H.|last2=Lund|first2=Thomas|website=TC Electronic A/S|location=Denmark|quote=inter-sample peaks may be considerably higher than 0dBFS.|access-date=2018-07-27|archive-date=2019-05-02|archive-url=https://web.archive.org/web/20190502034621/https://service.tcgroup.tc/media/Level_paper_AES109%281%29.pdf|url-status=dead}}<!-- possible replacement link: https://www.researchgate.net/publication/228898071_0dBFS_Levels_in_Digital_Mastering either the same paper or a subsequent paper by same authors --></ref> This can be prevented by careful [[digital-to-analog converter]] circuit design.<ref>{{cite web|url = http://www.cadenzarecording.com/papers/Digitaldistortion.pdf|title = Digital Distortion in CD's and DVD's: The Consequences of Traditional Digital Peak Meters|last = Aldrich|first = Nika|date = July 2003|publisher = Trillium Lane Labs|access-date = 20 November 2010|archive-url = https://web.archive.org/web/20100816061448/http://www.cadenzarecording.com/papers/Digitaldistortion.pdf|archive-date = 2010-08-16}}</ref> Measurements of the true inter-sample peak levels are notated as '''dBTP''' or '''dB TP''' ("decibels true peak").<ref>{{Cite web|url=https://www.itu.int/rec/R-REC-BS.1770-4-201510-I/en|title=BS.1770-4 (10/2015): Algorithms to measure audio programme loudness and true-peak audio level|website=International Telecommunication Union|access-date=2018-07-27|quote=Meters that ... use an oversampled sampling rate of at least 192 kHz, should indicate the result in the units of dB TP [which] signifies decibels relative to 100% full scale, true-peak measurement.}}</ref><ref>{{Cite web|url=https://www.bbc.co.uk/rd/publications/whitepaper202|title=Terminology for Loudness and Level dBTP, LU and all that - BBC R&D|website=BBC|date=January 2011 |language=en|access-date=2018-07-27|quote=As can be seen from the figure, if the peak sample values are 0 dBFS, the true peak will be higher than 0 dBTP.}}</ref>

== RMS levels ==
Since a peak measurement is not useful for qualifying the noise performance of a system,<ref>{{Cite journal|last=Davidson|first=J.|date=1961|title=Average vs RMS meters for measuring noise|journal=IRE Transactions on Audio|language=en-US|volume=AU-9|issue=4|pages=108–111|doi=10.1109/tau.1961.1166333|issn=0096-1981|quote=the conclusion is reached that the meaningful quantities are found by rms measurements. ... At this point it may be objected that other measurements, peak, or peak-to-peak voltage measurements in particular, are also significant. This is true, but not from the standpoint adopted here. Such measurements are applicable only to the field of nonlinear response, such as dielectric breakdown, etc.}}</ref> or measuring the [[loudness]] of an audio recording, for instance, RMS measurements are often used instead.

A potential for ambiguity exists when assigning a level on the dBFS scale to a waveform rather than to a specific amplitude, because some engineers follow the mathematical definition of RMS, which for sinusoidal signals is 3{{nnbsp}}dB below the peak value, while others choose the reference level so that RMS and peak measurements of a sine wave produce the same result.<ref>{{cite web
 | title = RMS Settings
 | work = Adobe Audition – User Guide for Windows
 | publisher = [[Adobe Systems|Adobe]]
 | year = 2003
 | url = http://download.adobe.com/pub/adobe/magic/audition/win/2.02/audition_user_guide.pdf#page=215
 | format = PDF
 | access-date = 2007-03-16
 | archive-url = https://web.archive.org/web/20070127205047/http://download.adobe.com/pub/adobe/magic/audition/win/2.02/audition_user_guide.pdf#page=215
 | archive-date = 2007-01-27
 | url-status = dead
 }} - Allows "0dB = FS Sine Wave" or "0dB = FS Square Wave"</ref><ref>
{{cite web
 | title = 0 Db Reference
 | work = Active Voice / Noise Level Monitor User's Guide
 | publisher = GL Communications, Inc.
 | url = http://www.gl.com/activevoicelevel.html
 | access-date = 2007-03-16
}} - "0 Db" reference can be either "FS Sine Wave" or "FS Square1 1Wave"</ref><ref name=":0">
{{Cite news
 |quote=This method yields a result of -3dB for a full scale sine wave and 0dB for a full scale square wave. Sound Forge uses this method.
 |url=https://www.digido.com/ufaqs/zero-dbfs-defined/
 |title=Zero dBFS Defined
 |last=Katz|first=Robert
 |date=2000-10-28
 |work=Digital Domain
 |access-date=2017-06-11
 |language=en-US
}}</ref><ref>
{{Cite news
 |quote=many software programs indicate level on virtual meters by means of a conventional RMS calculation, leading to a full scale sine wave reading -3.01 dB FS, which is incorrect in the context of this document.
 |url=https://www.atsc.org/recommended-practice/a85-techniques-for-establishing-and-maintaining-audio-loudness-for-digital-television/
 |title=A/85 – Techniques for Establishing and Maintaining Audio Loudness for Digital Television — ATSC
 |work=ATSC
 |access-date=2018-07-27
 |language=en-US
}}</ref><ref>
{{Cite news
 |url=http://productionadvice.co.uk/lufs-dbfs-rms/
 |title=LUFS, dBFS, RMS... WTF ?!? How to read the new loudness meters - Production Advice
 |date=2013-01-08
 |work=Production Advice
 |access-date=2018-07-27
 |language=en-US
}}</ref>

The unit '''dB FS''' or '''dBFS''' is defined in [[Audio Engineering Society|AES]] Standard AES17-1998,<ref>{{Cite web|url=http://www.aes.org/publications/standards/search.cfm?docID=21|title=AES Standard » AES17-2015: AES standard method for digital audio engineering - Measurement of digital audio equipment|website=www.aes.org|access-date=2016-04-29|quote=Because the definition of full scale is based on a sine wave, it will be possible with square-wave test signals to read as much as + 3,01 dB FS.}}</ref> IEC 61606,<ref>{{Cite web|url=https://www.sis.se/api/document/preview/571704/|title=IEC 61606-3:2008 Audio and audiovisual equipment - Digital audio parts - Basic measurement methods of audio characteristics - Part 3: Professional use|date=2008|website=International Electrotechnical Commission|language=en|access-date=2018-07-27|quote=the r.m.s. amplitude of a ... 997 Hz sinusoid whose peak positive sample just reaches positive digital full-scale ... is defined as 0 dB FS}}</ref> and ITU-T Recs. P.381<ref>{{Cite web|url=https://www.itu.int/rec/T-REC-P.381-201703-I/en|title=P.381 (03/17): Technical requirements and test methods for the universal wired headset or headphone interface of digital mobile terminals|date=2017|website=International Telecommunication Union|access-date=2018-07-27|quote=0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal}}</ref> and P.382,<ref>{{Cite web|url=https://www.itu.int/rec/T-REC-P.382-201607-I/en|title=P.382 (07/16): Technical requirements and test methods for multi-microphone wired headset or headphone interfaces of digital wireless terminals|website=International Telecommunication Union|access-date=2018-07-27|quote=0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal signal}}</ref> such that the RMS value of a full-scale '''sine''' wave is designated 0{{nnbsp}}dB FS.  This means a full-scale square wave would have an RMS value of +3{{nnbsp}}dB FS.<ref>[http://www.analog.com/static/imported-files/application_notes/an_938.pdf Digital and Analog Measurement Units for Digital CMOS Microphone Preamplifier ASICs] ([[Analog Devices]]) - "The definition of 0 dBFS as a full-scale sine wave is used by several audio analyzers, and the rms and peak values in the digital domain for a sine wave are equal for these analyzers. … Thus, a square wave whose top and bottom are at the maximum digital codes has an rms value of 1.414 FFS or 3.01 dBFS"</ref><ref>{{cite web|url=http://www.tonmeister.ca/main/textbook/intro_to_sound_recordingch11.html#x42-77200010.1.5|title=10 Audio Recording|date=23 October 2011|publisher=Tonmeister|access-date=30 January 2016}}</ref>  This convention is used in [[Wolfson Microelectronics|Wolfson]]<ref>{{Cite web|url=http://origin.cirrus.com/en/pubs/proDatasheet/WM7216E_v4.0.pdf|title=WM7216E datasheet|date=May 2016|quote=Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3dBFS.}}{{Dead link|date=August 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> and [[Cirrus Logic]]<ref>{{Cite web|url=https://d3uzseaevmutz1.cloudfront.net/pubs/proDatasheet/CS7250B_PP1.pdf|title=CS7250B datasheet|quote=Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3 dBFS.}}</ref> digital microphone specs, etc.

The unit '''dBov''' is defined in the ITU-T G.100.1 telephony standard such that the RMS value of a full-scale '''square''' wave is designated 0{{nnbsp}}dBov.<ref name=":2" /><ref>{{Cite journal|url=https://tools.ietf.org/html/rfc3389|title=Real-time Transport Protocol (RTP) Payload for Comfort Noise (CN)|last=Zopf|first=Robert|website=tools.ietf.org|year=2002 |doi=10.17487/RFC3389 |access-date=2016-04-30|quote=For example, in the case of a u-law system, the reference would be a square wave ... and this ... represents 0dBov}}</ref>  All possible dBov measurements are negative numbers, and a sine wave cannot exist at a larger RMS value than −3 dBov without [[Clipping (music)|clipping]].<ref name=":2">{{Cite web|url=https://www.itu.int/rec/T-REC-G.100.1-201506-I/en|title=G.100.1 (06/15): The use of the decibel and of relative levels in speechband telecommunications|website=International Telecommunication Union|access-date=2018-07-27|quote=The level of a ''tone'' with a digital amplitude (peak value) of x<sub>''over''</sub> is therefore L= –3.01 dBov.}}</ref> This unit can be applied to both analog and digital systems.<ref name=":2" />  This convention is the basis for the ITU's [[LUFS]] loudness unit,<ref>{{Cite web|url=https://www.itu.int/rec/R-REC-BS.1770-4-201510-I/en|title=BS.1770-4 (10/2015): Algorithms to measure audio programme loudness and true-peak audio level|date=2015|website=International Telecommunication Union|access-date=2018-07-27|quote=If a 0 dB FS, 1 kHz ... sine wave is applied to the ... input, the indicated loudness will equal −3.01 LKFS.}}</ref> and is also used in Sound Forge<ref name=":0" /> and Euphonix meters,<ref name=":1">{{Cite web|url=http://connect.euphonix.com/documents/S5_App_1_Metering.pdf|title=Application Note 1: System 5 Metering: Peak vs. Average|date=January 2002|quote=On a logarithmic dB scale, the difference between a sine wave's peak and RMS average level is 3 dB. Euphonix bases its metering on the Audio Precision measurement system, which adheres to the RMS average technique.}}</ref> and Analog Devices digital microphone specs<ref>{{cite web|url=http://www.analog.com/library/analogdialogue/archives/46-05/understanding_microphone_sensitivity.html|title=Understanding Microphone Sensitivity|publisher=Analog|quote=so a digital microphone’s output must be scaled from peak to rms by lowering the dBFS value. For a sinusoidal input, the rms level is 3 dB (the logarithmic measure of (FS√2) below the peak level ... A 94 dB SPL sinusoidal input signal will give a –26 dBFS peak output level, or a –29 dBFS rms level.|access-date=30 January 2016}}</ref> (though referred to as "dBFS").

== Dynamic range ==
The measured [[dynamic range]] (DR) of a digital system is the ratio of the full scale signal level to the RMS [[noise floor]]. The theoretical minimum noise floor is caused by [[quantization noise]]. This is usually modeled as a uniform random fluctuation between −{{frac|1|2}} [[Least significant bit|LSB]] and +{{frac|1|2}} LSB. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)<ref>{{cite book
  | last = Watkinson
  | first = John
  | title = The Art of Digital Audio 3rd Edition
  | publisher = Focal Press
  | year = 2001
  | isbn = 978-0-240-51587-8}}</ref>

As the [[dynamic range]] is measured relative to the RMS level of a full scale sine wave, the dynamic range and the level of this quantization noise in dBFS can both be estimated with the same formula (though with reversed sign):
:<math>
\mathrm{DR} = \mathrm{SNR} = 20\log_{10}{\left(2^n \sqrt{\tfrac{3}{2}}\right)} \approx 6.0206 n + 1.761
</math>

The value of ''n'' equals the resolution of the system in bits or the resolution of the system minus 1{{nbsp}}bit (the measure error).  For example, a 16-bit system has a theoretical minimum noise floor of −98.09{{nnbsp}}dBFS relative to a full-scale sine wave:
:<math>
\mathrm{DR} = \mathrm{SNR} = 20\log_{10}{\left(2^{16} \sqrt{\tfrac{3}{2}}\right)} \approx 6.0206 \cdot 16 + 1.761 \approx 98.09\,
</math>

In any real converter, [[dither]] is added to the signal before sampling. This removes the effects of non-uniform [[quantization error]], but increases the minimum noise floor.

==History==
The phrase "dB below full scale" has appeared in print since the 1950s,<ref>{{Cite book|url=https://books.google.com/books?id=McoiAQAAMAAJ|title=Automatic Control|date=1957-01-01|publisher=Reinhold Publishing Corporation|language=en}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=BS5IAQAAIAAJ|title=Hewlett-Packard Journal|date=1962-01-01|publisher=Hewlett-Packard Company|language=en}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=SXwTAQAAMAAJ|title=The General Radio Experimenter|date=1969-01-01|publisher=General Radio Company|language=en}}</ref> and the term "dBFS" has been used since 1977.<ref>{{Cite journal|last=Robert|first=Talambiras|date=1977-05-01|title=Some Considerations in the Design of Wide-Dynamic-Range Audio Digitizing Systems|url=http://www.aes.org/e-lib/browse.cfm?elib=3129|language=en|quote=It is convenient when working with A/D converters to define a 0 dB reference for a full-scale-to-full-scale sine wave. ... The quantizing noise in the Nyquist bandwidth for a 16 bit converter would be -98.08dbFS}}</ref>

Although the decibel (dB) is permitted for use alongside units of the [[International System of Units]] (SI), the dBFS is not.<ref>[http://physics.nist.gov/cuu/pdf/sp811.pdf Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811]</ref>

== Analog levels ==
dBFS is not defined for analog levels, according to standard AES-6id-2006. No single standard converts between digital and analog levels, mostly due to the differing capabilities of different equipment. The amount of oversampling also affects the conversion with values that are too low having significant error.   The conversion level is chosen as the best compromise for the typical headroom and signal-to-noise levels of the equipment in question. Examples:<ref>http://wiki.ibs.org.uk/faq/index.php?title=dBFS#dBFS{{Dead link|date=November 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite web|url=http://www.sengpielaudio.com/calculator-db-volt.htm|title= Decibel (dB) level conversion to volt|author=Eberhard Sengpiel|publisher=Sengpiel Audio|access-date=30 January 2016}}</ref><ref>http://www.broadcastpapers.com/whitepapers/paper_loader.cfm?pid=393{{Dead link|date=July 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

* EBU R68 is used in most European countries, specifying +18{{nnbsp}}[[dBu]] at 0{{nnbsp}}dBFS.
* In Europe, the EBU recommend that −18{{nnbsp}}dBFS equates to the ''[[alignment level]]''.
** UK broadcasters, ''alignment level'' is taken as 0{{nnbsp}}dBu (PPM{{nbsp}}4 or −4{{nbsp}}VU)
** The American SMPTE standard defines −20{{nnbsp}}dBFS as the ''alignment level''.
* European and UK calibration for {{clarify|text=Post & Film|date=September 2019}} is −18{{nnbsp}}dBFS = 0{{nbsp}}VU.
* US installations use +24{{nnbsp}}dBu for 0{{nnbsp}}dBFS.
* American and Australian Post: −20{{nnbsp}}dBFS = 0{{nbsp}}VU = +4{{nnbsp}}dBu.
* In Japan, France, and some other countries, converters may be calibrated for +22{{nnbsp}}dBu at 0{{nnbsp}}dBFS.
* BBC specification: −18{{nnbsp}}dBFS = PPM{{nbsp}}"4" = 0{{nnbsp}}dBu
* German ARD and studio, PPM{{nbsp}}+6{{nnbsp}}dBu = −10 (−9){{nbsp}}dBFS. +16 (+15){{nbsp}}dBu = 0{{nnbsp}}dBFS. No VU.
* Belgium VRT: 0&nbsp;dB (VRT ref.) = +6{{nnbsp}}dBu; −9{{nnbsp}}dBFS = 0&nbsp;dB (VRT ref.); 0{{nnbsp}}dBFS = +15{{nnbsp}}dBu.

== See also ==
*[[Audio bit depth]]
*[[Bit rate]]
*[[Full scale]]

== References ==
{{reflist|30em}}

== External links ==
*[http://www.aes.org/par/d/#0_dBFS AES Pro Audio Reference definition of dBFS]
*[http://www.sweetwater.com/insync/dbfs/ dBFS – Sweetwater glossary]
{{Decibel}}

[[Category:Digital audio]]
[[Category:Logarithmic scales of measurement]]

[[ru:DBFS]]