View source for Physics:A-weighting

{{Short description|Frequency response curves used in sound pressure level measurement}}
[[File:Acoustic weighting curves (1).svg|thumb|400px|right|A graph of the A-, B-, C- and D-weightings across the frequency range 10&nbsp;Hz&nbsp;&ndash;&nbsp;20&nbsp;kHz]]
[[File:Illustration of A weighting.ogv|thumb|400px|right|Video illustrating A-weighting by analyzing a sine sweep (contains audio)]]

'''A-weighting''' is the most commonly used of a [[Physics:Weighting filter|family of curves]] defined in the International standard [[Organization:International Electrotechnical Commission|IEC]] 61672:2003 and various national standards relating to the measurement of [[Physics:Sound pressure level|sound pressure level]].<ref name="Meyer-Bisch" /> A-weighting is applied to instrument-measured sound levels in an effort to account for the relative [[Physics:Loudness|loudness]] perceived by the human ear, as the ear is less sensitive to low audio frequencies.  It is employed by arithmetically adding a table of values, listed by [[Physics:Octave band|octave]] or third-octave bands, to the measured sound pressure levels in [[Physics:Decibel|dB]]. The resulting octave band measurements are usually added (logarithmic method) to provide a single A-weighted value describing the sound; the units are written as dB(A).  Other weighting sets of values – B, C, D and now Z – are discussed below.

The curves were originally defined for use at different average sound levels, but A-weighting, though originally intended only for the measurement of low-level sounds (around 40 [[Physics:Phon|phon]]), is now commonly used for the measurement of [[Physics:Environmental noise|environmental noise]] and industrial noise, as well as when assessing potential hearing damage and other noise health effects at all sound levels; indeed, the use of A-frequency-weighting is now mandated for all these measurements, because decades of field experience have shown a very good correlation with occupational deafness in the frequency range of human speech. It is also used when measuring low-level noise in audio equipment, especially in the United States.{{Citation needed lead|date=July 2010}} In Britain, Europe and many other parts of the world, broadcasters and audio engineers{{Who|date=July 2010}} more often use the [[Physics:ITU-R 468 noise weighting|ITU-R 468 noise weighting]], which was developed in the 1960s based on research by the BBC and other organizations.  This research showed that our ears respond differently to random noise, and the equal-loudness curves on which the A, B and C weightings were based are really only valid for pure single tones.{{citation needed lead|date=July 2012}}

== History ==

A-weighting began with work by [[Engineering:Fletcher–Munson curves|Fletcher and Munson]] which resulted in their publication, in 1933, of a set of [[Physics:Equal-loudness contour|equal-loudness contour]]s. Three years later these curves were used in the first American standard for [[Physics:Sound level meter|sound level meter]]s.<ref name="Pierre_2004" /> This ANSI standard, later revised as ANSI S1.4-1981, incorporated B-weighting as well as the A-weighting curve, recognising the unsuitability of the latter for anything other than low-level measurements. But B-weighting has since fallen into disuse. Later work, first by Zwicker and then by Schomer, attempted to overcome the difficulty posed by different levels, and work by the BBC resulted in the CCIR-468 weighting, currently maintained as ITU-R 468 noise weighting, which gives more representative readings on noise as opposed to pure tones.{{Citation needed|date=March 2009}}

== Deficiencies ==
A-weighting is valid to represent the sensitivity of the human ear as a function of the frequency of pure tones. The A-weighting was based on the 40-phon [[Engineering:Fletcher–Munson curves|Fletcher–Munson curves]], which represented an early determination of the [[Physics:Equal-loudness contour|equal-loudness contour]] for human hearing. However, because decades of field experience have shown a very good correlation between the A scale and occupational deafness in the frequency range of human speech,{{citation needed|date=April 2022}} this scale is employed in many jurisdictions to evaluate the risks of occupational deafness and other auditory problems related to signals or speech intelligibility in noisy environments.

Because of perceived discrepancies between early and more recent determinations, the [[Organization:International Organization for Standardization|International Organization for Standardization]] (ISO) revised its standard curves as defined in ISO 226, in response to the recommendations of a study coordinated by the Research Institute of Electrical Communication, Tohoku University, Japan. The study produced new curves by combining the results of several studies, by researchers in Japan, Germany, Denmark, UK, and USA. (Japan was the greatest contributor with about 40% of the data.) This has resulted in the recent acceptance of a new set of curves standardized as ISO 226:2003. The report comments on the surprisingly large differences, and the fact that the original Fletcher–Munson contours are in better agreement with recent results than the Robinson-Dadson, which appear to differ by as much as 10–15&nbsp;dB especially in the low-frequency region, for reasons that are not explained. The report also shows that the 40-phon Fletcher-Munson contour is in better agreement with the updated 60-phon contour incorporated into ISO 226:2003, which challenges the common assertion that A-weighting represents loudness only for quiet sounds.<ref name="NEDO" />

Nevertheless, A-weighting would be a better match to the loudness curve if it fell much more steeply above 10&nbsp;kHz, and it is likely that this compromise came about because steep filters were difficult to construct in the early days of electronics.{{Citation needed|date=May 2010}} Nowadays, no such limitation need exist, as demonstrated by the ITU-R 468 curve. If A-weighting is used without further band-limiting it is possible to obtain different readings on different instruments when ultrasonic, or near ultrasonic noise is present. Accurate measurements therefore require a 20&nbsp;kHz low-pass filter to be combined with the A-weighting curve in modern instruments. This is defined in IEC 61012 as AU weighting and while very desirable, is rarely fitted to commercial sound level meters.

== {{anchor|B|C|D|G|Z}}B-, C-, D-, G- and Z-weightings ==

A-frequency-weighting is mandated by the international standard IEC&nbsp;61672 to be fitted to all sound level meters and are approximations to the equal loudness contours given in ISO&nbsp;226.<ref name="Rimell-Mansfield-Paddan_2015" /> The old B- and D-frequency-weightings have fallen into disuse, but many sound level meters provide for C frequency-weighting and its fitting is mandated &mdash; at least for testing purposes &mdash; to precision (Class one) sound level meters. D-frequency-weighting was specifically designed for use when measuring high-level aircraft noise in accordance with the IEC 537 measurement standard. The large peak in the D-weighting curve is not a feature of the equal-loudness contours, but reflects the fact that humans hear random noise differently from pure tones, an effect that is particularly pronounced around 6&nbsp;kHz. This is because individual neurons from different regions of the [[Medicine:Cochlea|cochlea]] in the inner ear respond to narrow bands of frequencies, but the higher frequency neurons integrate a wider band and hence signal a louder sound when presented with noise containing many frequencies than for a single pure tone of the same pressure level.{{Citation needed|date=March 2011}} 

Following changes to the ISO standard, D-frequency-weighting by itself should now only be used for non-bypass-type jet engines, which are found only on military aircraft and not on commercial aircraft.  For this reason, today A-frequency-weighting is now mandated for light civilian aircraft measurements, while a more accurate loudness-corrected weighting [[Physics:EPNdB|EPNdB]] is required for certification of large transport aircraft.<ref name="ICAO" /> D-weighting is the basis for the measurement underlying EPNdB.
  
Z- or ZERO frequency-weighting was introduced in the International Standard IEC&nbsp;61672 in 2003 and was intended to replace the "Flat" or "Linear" frequency weighting often fitted by manufacturers. This change was needed as each sound level meter manufacturer could choose their own low and high frequency cut-offs (&ndash;3&nbsp;dB) points, resulting in different readings, especially when peak sound level was being measured{{Citation needed|date=June 2022}}. It is a flat frequency response between 10&nbsp;Hz and 20&nbsp;kHz ±1.5&nbsp;dB.<ref name="Lauer_2012" />{{Not in citation|date=June 2022}} As well, the C-frequency-weighting, with &ndash;3&nbsp;dB points at 31.5&nbsp;Hz and 8&nbsp;kHz did not have a sufficient bandpass to allow the sensibly correct measurement of true peak noise (Lpk).

G-weighting is used for measurements in the [[Physics:Infrasound|infrasound]] range from 8&nbsp;Hz to about 40&nbsp;Hz.<ref name="LUBW_2016"/>

B- and D-frequency-weightings are no longer described in the body of the standard IEC&nbsp;61672:2003, but their frequency responses can be found in the older IEC&nbsp;60651, although that has been formally withdrawn by the International Electrotechnical Commission in favour of IEC&nbsp;61672:2003. The frequency weighting tolerances in IEC&nbsp;61672 have been tightened over those in the earlier standards IEC&nbsp;179 and IEC&nbsp;60651 and thus instruments complying with the earlier specifications should no longer be used for legally required measurements.

== Environmental and other noise measurements ==
[[File:Atlas Copco XAHS 347-pic7-Max. sound power level.jpg|thumb|100px|Label related to a portable air compressor]]
A-weighted [[Physics:Decibel|decibel]]s are abbreviated '''dB(A)''' or '''dBA.''' When acoustic (calibrated microphone) measurements are being referred to, then the units used will be [[Physics:Decibel|dB]] [[Physics:Sound pressure level|SPL]] referenced to
20 micropascals = 0&nbsp;dB SPL.<ref name="NB_dBa" group="nb" />

The A-weighting curve has been widely adopted for [[Physics:Environmental noise|environmental noise]] measurement, and is standard in many sound level meters. The A-weighting system is used in any measurement of environmental noise (examples of which include roadway noise, rail noise, [[Engineering:Aircraft noise|aircraft noise]]). A-weighting is also in common use for assessing potential hearing damage caused by loud noise, including [[Physics:Noise dosimeter|noise dose]] measurements at work. A noise level of more than 85&nbsp;dB(A) each day increases the risk factor for hearing damage.

A-weighted [[Physics:Sound power|sound power levels]] ''L''<sub>WA</sub> are increasingly found on sales literature for domestic appliances such as refrigerators, freezers and computer fans. 
The expected [[Physics:Sound pressure|sound pressure level]] to be measured at a given distance as SPL with a [[Physics:Sound level meter|sound level meter]] can with some simplifications be calculated from the [[Physics:Sound power|sound power level]]. 
In Europe, the A-weighted noise level is used for instance for normalizing the noise of tires on cars.

Noise exposure for visitors of venues with loud music is usually also expressed in dB(A), although the presence of high levels of low frequency noise does not justify this.

== Audio reproduction and broadcasting equipment ==

[[Image:Lindos3.svg|400px|right]]

Although the A-weighting curve, in widespread use for [[Physics:Noise measurement|noise measurement]], is said to have been based on the 40-phon Fletcher-Munson curve, research in the 1960s demonstrated that determinations of equal-loudness made using pure tones are not directly relevant to our perception of noise.<ref name="Bauer-Torick_1966" /> This is because the cochlea in our inner ear analyses sounds in terms of spectral content, each [[Biology:Hair cell|hair cell]] responding to a narrow band of frequencies known as a critical band.{{citation needed|date=June 2019}} The high-frequency bands are wider in absolute terms than the low-frequency bands, and therefore 'collect' proportionately more power from a noise source.{{citation needed|date=June 2019}} However, when more than one critical band is stimulated, the outputs of the various bands are summed by [[Biology:Human brain|the brain]] to produce an impression of loudness. For these reasons equal-loudness curves derived using noise bands show an upwards tilt above 1&nbsp;kHz and a downward tilt below 1&nbsp;kHz when compared to the curves derived using pure tones.

This enhanced sensitivity to noise in the region of 6&nbsp;kHz became particularly apparent in the late 1960s with the introduction of compact cassette recorders and Dolby-B noise reduction. A-weighted noise measurements were found to give misleading results because they did not give sufficient prominence to the 6&nbsp;kHz region where the noise reduction was having greatest effect, and did not sufficiently attenuate noise around 10&nbsp;kHz and above (a particular example is with the 19&nbsp;kHz pilot tone on FM radio systems which, though usually inaudible is not sufficiently attenuated by A-weighting, so that sometimes one piece of equipment would even measure worse than another and yet sound better, because of differing spectral content.

[[Physics:ITU-R 468 noise weighting|ITU-R 468 noise weighting]] was therefore developed to more accurately reflect the subjective loudness of all types of noise, as opposed to tones. This curve, which came out of work done by the BBC Research Department, and was standardised by the CCIR and later adopted by many other standards bodies ([[Organization:International Electrotechnical Commission|IEC]], BSI) and, {{As of|2006|lc=on}}, is maintained by the ITU. It became widely used in Europe, especially in broadcasting, and was adopted by [[Organization:Dolby Laboratories|Dolby Laboratories]] who realised its superior validity for their purposes when measuring noise on film soundtracks and compact cassette systems. Its advantages over A-weighting are less accepted in the US, where the use of A-weighting still predominates.{{Citation needed|date=March 2009}} It is used by broadcasters in Britain, Europe, and former countries of the British Empire such as Australia and South Africa.

== Function realisation of some common weightings ==
The standard<ref name="IEC61672" /> defines weightings (<math>A(f), C(f)</math>) in dB units by tables with tolerance limits (to allow a variety of implementations). Additionally, the standard describes weighting functions <math>R_X(f)</math><ref name="IEC61672" /> to calculate the weightings. The weighting function <math>R_X(f)</math> is applied to the [[Physics:Sound pressure|amplitude spectrum]] (not the [[Physics:Sound intensity|intensity spectrum]]) of the unweighted sound level. The offsets ensure the normalisation to 0&nbsp;dB at 1000&nbsp;Hz. Appropriate weighting functions are:<ref name="CS_2004" />

===A===
:<math>\begin{align}
  R_A(f) &= {12194^2 f^4 \over \left(f^2 + 20.6^2\right)\ \sqrt{\left(f^2 + 107.7^2\right)\left(f^2 + 737.9^2\right)}\ \left(f^2 + 12194^2\right)}\ ,\\[3pt]
    A(f) &= 20\log_{10}\left(R_A(f)\right) - 20\log_{10}\left(R_A(1000)\right) \\
         &\approx 20\log_{10}\left(R_A(f)\right) + 2.00
\end{align}</math><ref name="IEC61672" />

===B===
: <math>\begin{align}
  R_B(f) &= {12194^2 f^3\over \left(f^2 + 20.6^2\right)\ \sqrt{\left(f^2 + 158.5^2\right)} \  \left(f^2 + 12194^2\right)}\ ,\\[3pt]
    B(f) &= 20\log_{10}\left(R_B(f)\right) - 20\log_{10}\left(R_B(1000)\right) \\
         &\approx 20\log_{10}\left(R_B(f)\right) + 0.17
\end{align}</math>

===C===
:<math>\begin{align}
  R_C(f) &= {12194^2 f^2 \over \left(f^2 + 20.6^2\right)\ \left(f^2 + 12194^2\right)}\ ,\\[3pt]
    C(f) &= 20\log_{10}\left(R_C(f)\right) - 20\log_{10}\left(R_C(1000)\right) \\[3pt]
         &\approx 20\log_{10}\left(R_C(f)\right) + 0.06
\end{align}</math><ref name="IEC61672" />

===D===
: <math>\begin{align}
    h(f) &= \frac{\left(1037918.48 - f^2\right)^2 + 1080768.16\,f^2}{\left(9837328 - f^2\right)^2 + 11723776\,f^2} \\[3pt]
  R_D(f) &= \frac{f}{6.8966888496476 \cdot 10^{-5}} \sqrt{\frac{h(f)}{\left(f^2 + 79919.29\right)\left(f^2 + 1345600\right)}} \\
    D(f) &= 20\log_{10}\left(R_D(f)\right).
\end{align}</math><ref name="Aarts_1992" />

== Transfer function equivalent==
The gain curves can be realised<ref name="PTP" /> by the following s-domain [[Transfer function|transfer function]]s. They are not defined in this way though, being defined by tables of values with tolerances in the standards documents, thus allowing different realisations:{{Citation needed|date=March 2011}}

===A===
:<math>H_\text{A}(s) \approx {k_\text{A} \cdot s^4 \over (s + 129.4)^2\quad(s + 676.7)\quad (s + 4636)\quad (s + 76617)^2}</math>
:''k''<sub>A</sub> ≈ 7.39705 × 10<sup>9</sup>

===B===
:<math>H_\text{B}(s) \approx {k_\text{B} \cdot s^3\over(s + 129.4)^2\quad (s + 995.9)\quad (s + 76617)^2}</math>
:''k''<sub>B</sub> ≈ 5.99185 × 10<sup>9</sup>

===C===
:<math>H_\text{C}(s) \approx {k_\text{C} \cdot s^2\over(s + 129.4)^2\quad (s + 76617)^2}</math>
:''k''<sub>C</sub> ≈ 5.91797 × 10<sup>9</sup>

===D===
:<math>H_\text{D}(s) \approx {k_\text{D} \cdot s \cdot \left(s^2 + 6532 s + 4.0975 \times 10^7\right)\over(s + 1776.3)\quad (s + 7288.5)\quad \left(s^2 + 21514 s + 3.8836 \times 10^8\right)}</math>
:''k''<sub>D</sub> ≈ 91104.32

The ''k''-values are constants that are used to normalize the function to a gain of 1 (0&nbsp;dB). The values listed above normalize the functions to 0&nbsp;dB at 1&nbsp;kHz, as they are typically used. (This normalization is shown in the image.)

== See also ==
* [[Physics:Noise|Noise]]
* Signal noise
* [[Physics:ITU-R 468 noise weighting|ITU-R 468 noise weighting]]
* M-weighting
* [[Physics:Psophometric weighting|Psophometric weighting]]
* Audio quality measurement
* [[Physics:Noise pollution|Noise pollution]]
* [[Earth:Noise regulation|Noise regulation]]
* [[Physics:Headroom (audio signal processing)|Headroom]]
* Rumble measurement
* [[Physics:Weighting filter|Weighting filter]]
* [[Physics:Weighting curve|Weighting curve]]
* [[Physics:Luminous efficiency function|Luminous efficiency function]], the light equivalent
* [[Engineering:LKFS|LKFS]]

== Notes ==
{{Reflist|group="nb"|refs=
<ref name="NB_dBa" group="nb">''dBrn adjusted'' is not a synonym for dB(A), but for dBa. (In telecommunications dBa denotes "decibels adjusted", i.e. weighted absolute noise power, which has nothing to do with A-weighting.)</ref>
}}

== References ==
{{Reflist|refs=
<ref name="Meyer-Bisch">{{Cite journal |last=Meyer-Bisch |first=Christian |year=2005 |title=[Measuring noise] |journal=Médecine/Sciences |volume=21 |issue=5 |pages=546–550 |doi=10.1051/medsci/2005215546 |issn=0767-0974 |pmid=15885208 |doi-access=free}}</ref>
<ref name="Pierre_2004">{{Cite web |last=Pierre, Jr. |first=Richard L. St. |date=July 2004 |title=The Impact of A-weighting Sound Pressure Level Measurements during the Evaluation of Noise Exposure |url=http://storeycountywindfarms.org/ref3_Impact_Sound_Pressure.pdf |access-date=2011-09-13 |author-first2=Daniel J. |author-last2=Maguire}}</ref>
<ref name="NEDO">{{Cite web |title=Precise and Full-range Determination of Two-dimensional Equal Loudness Contours |url=http://www.nedo.go.jp/itd/grant-e/report/00pdf/is-01e.pdf |archive-url=https://web.archive.org/web/20070927210848/http://www.nedo.go.jp/itd/grant-e/report/00pdf/is-01e.pdf |archive-date=2007-09-27}}</ref>
<ref name="Rimell-Mansfield-Paddan_2015">{{Cite journal |year=2015 |title=Design of digital filters for frequency weightings (A and C) required for risk assessments of workers exposed to noise |journal=Industrial Health |volume=53 |issue=53 |pages=21–27 |doi=10.2486/indhealth.2013-0003 |pmc=4331191 |pmid=25224333 |author-last1=Rimell |author-first1=Andrew |author-last2=Mansfield |author-first2=Neil |author-last3=Paddan |author-first3=Gurmail |s2cid=13997453}}</ref>
<ref name="ICAO">{{Cite web |title=BIP_2_2_jb ZIP file |url=http://www.icao.int/Meetings/EnvironmentalWorkshops/Documents/NoiseCertificationWorkshop-2004/BIP_2_2_jb.pdf}}</ref>
<ref name="Lauer_2012">{{Cite journal |year=2012 |title=MRI Acoustic Noise Can Harm Experimental and Companion Animals |journal=Journal of Magnetic Resonance Imaging |volume=36 |issue=3 |pages=743–747 |doi=10.1002/jmri.23653 |pmid=22488793 |doi-access=free |author-last1=Lauer |author-first1=Amanda |author-last2=El-Sharkawy |author-first2=AbdEl-Monem M. |author-last3=Kraitchman |author-first3=Dara |author-last4=Edelstein |author-first4=William |s2cid=7436249}}</ref>
<ref name="Bauer-Torick_1966">{{Cite journal |year=1966 |title=Researches in loudness measurement |journal=IEEE Transactions on Audio and Electroacoustics |volume=14 |issue=3 |pages=141–151 |doi=10.1109/TAU.1966.1161864 |author-last1=Bauer |author-first1=B. |author-last2=Torick |author-first2=E.}}</ref>
<ref name="IEC61672">{{Cite book |title=IEC 61672-1:2013 Electroacoustics - Sound level meters - Part 1: Specifications |date=2013 |publisher=IEC}}</ref>
<ref name="CS_2004">{{Cite web |year=2004 |title=Frequency weighting equations |url=http://www.cross-spectrum.com/audio/weighting.html |url-status=live |archive-url=https://web.archive.org/web/20110617080228/http://www.cross-spectrum.com/audio/weighting.html |archive-date=2011-06-17 |publisher=Cross Spectrum}}</ref>{{Unreliable source?|date=March 2011}}
<ref name="Aarts_1992">{{Cite journal |date=1 March 1992 |title=A Comparison of Some Loudness Measures for Loudspeaker Listening Tests |url=https://www.aes.org/e-lib/browse.cfm?elib=7054 |url-status=live |journal=[[Organization:Audio Engineering Society|Audio Engineering Society]] |volume=40 |issue=3 |pages=142–146 |url-access=subscription |archive-url=https://web.archive.org/web/20221027155213/https://www.aes.org/e-lib/browse.cfm?elib=7054 |archive-date=2022-10-27 |access-date=2022-10-27 |author-first=Ronald M. |author-last=Aarts}}</ref>
<ref name="PTP">{{Cite web |title=Noise Measurement Briefing |url=http://www.ptpart.co.uk/show.php?contentid=70 |archive-url=https://web.archive.org/web/20080630083107/http://www.ptpart.co.uk/show.php?contentid=70 |archive-date=2008-06-30 |publisher=Product Technology Partners Ltd.}}</ref>
<ref name="LUBW_2016">{{Cite web |date=February 2020 |orig-date=2016-02-26 |editor-last=Ratzel |editor-first=U. |editor2-last=Bayer |editor2-first=O. |editor3-last=Brachat |editor3-first=P. |editor4-last=Hoffmann |editor4-first=M. |editor5-last=Jänke |editor5-first=K. |editor6-last=Kiesel |editor6-first=K.-J. |editor7-last=Mehnert |editor7-first=C. |editor8-last=Scheck |editor8-first=C. |editor9-last=Westerhausen |editor9-first=C. |title=Tieffrequente Geräusche inkl. Infraschall von Windkraftanlagen und anderen Quellen - Bericht über Ergebnisse des Messprojekts 2013-2015 |url=https://pudi.lubw.de/detailseite/-/publication/84558<!--http://www4.lubw.baden-wuerttemberg.de/servlet/is/257896/tieffrequente_geraeusche_inkl_infraschall.pdf?command=downloadContent&filename=tieffrequente_geraeusche_inkl_infraschall.pdf--> |access-date=2021-06-07 |publisher=Landesanstalt für Umwelt, Messungen und Naturschutz Baden-Württemberg (LUBW), Referat 34 – Technischer Arbeitsschutz, Lärmschutz |pages=10–11, 13, 17, 22–24, 27–28, 32–33, 38–39, 43–44, 49, 90 |language=de |quote=Für den Bereich des Infraschalls gibt es eine eigene Frequenzbewertung, die so genannte G-Bewertung. Entsprechend bewertete Pegel werden als dB(G) – „Dezibel G“ – angegeben. Bekannter ist die A-Bewertung von Geräuschen als dB(A) – „Dezibel A“ –, die dem Hörempfinden des Menschen nachempfunden ist. Die G-Bewertung hat ihren Schwerpunkt bei 20&nbsp;Hz. Zwischen 10&nbsp;Hz und 25&nbsp;Hz werden Pegel verstärkt, darunter und darüber fällt die Bewertungskurve rasch ab. Zweck der G-Bewertung ist es, eine Situation im Hinblick auf tiefe Frequenzen bzw. Infraschall mit einer einzigen Zahl zu charakterisieren. Ein Nachteil ist, dass Frequenzen unterhalb 8&nbsp;Hz und oberhalb 40&nbsp;Hz kaum mehr einen Beitrag leisten. |edition=3 |location=Karlsruhe, Germany |editor10-first=K.-G. |editor10-last=Krapf |editor11-first=L. |editor11-last=Herrmann |editor12-first=J. |editor12-last=Blaul |quote-page=90}} [https://web.archive.org/web/20210502101737/https://www.lubw.baden-wuerttemberg.de/-/bericht-tieffrequente-gerausche-und-infraschall-von-windkraftanlagen-und-anderen-quellen-veroffentlicht-] (104 pages)</ref>
}}

== Further reading ==
* ''Audio Engineer's Reference Book'', 2nd Ed 1999, edited Michael Talbot Smith, Focal Press
* ''An Introduction to the Psychology of Hearing'' 5th ed, Brian C. J. Moore, Elsevier Press

== External links ==
* [https://web.archive.org/web/20130225220126/http://www.ptpart.co.uk/noise-measurement-briefing/ Noise Measurement Briefing]. Archived from [http://www.ptpart.co.uk/noise-measurement-briefing/ the original] on 2013-02-25.
* [http://sound.whsites.net/project17.htm A-weighting filter circuit for audio measurements] {{Webarchive|url=https://web.archive.org/web/20161231170415/http://sound.whsites.net/project17.htm |date=2016-12-31  }}
* [http://www.beis.de/Elektronik/AudioMeasure/WeightingFilters.html Weighting Filter Set] Circuit diagrams
* [http://www.aes.org/par/w/#weighting_filters AES pro audio reference definition of "weighting filters"]
* [http://www.cross-spectrum.com/audio/weighting.html Frequency Weighting Equations]
* [https://lindos.co.uk/articles/a-weighting-in-detail A-weighting in detail]
* [https://web.archive.org/web/20070922043605/http://www.diracdelta.co.uk/science/source/a/w/aweighting/source.html A-Weighting] Equation and online calculation
* [http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel6/8337/26056/01161864.pdf?tp=&isnumber=26056&arnumber=1161864 Researches in loudness measurement by CBS using noise bands, 1966 IEEE Article]
* [https://www.aes.org/e-lib/browse.cfm?elib=7054 Comparison of some loudness measures for loudspeaker listening tests (Aarts, JAES, 1992)] PDF containing algorithm for ABCD filters

[[Category:Sound]]
[[Category:Audio engineering]]
[[Category:Noise]]
[[Category:Acoustics]]

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{{Sourceattribution|A-weighting}}