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from <a href="/w/index.php?title=Full-scale&redirect=no" class="mw-redirect" title="Full-scale">Full-scale</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Maximum amplitude a system can represent</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Full_Scale_(disambiguation)" class="mw-redirect mw-disambig" title="Full Scale (disambiguation)">Full Scale (disambiguation)</a>.</div> <p>In <a href="/wiki/Electronics" title="Electronics">electronics</a> and <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a>, <b>full scale</b> represents the maximum <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> a system can represent. </p><p>In <a href="/wiki/Digital_system" class="mw-redirect" title="Digital system">digital systems</a>, a signal is said to be at <b>digital full scale</b> when its magnitude has reached the maximum representable value. Once a signal has reached digital full scale, all <a href="/wiki/Headroom_(audio_signal_processing)" title="Headroom (audio signal processing)">headroom</a> has been utilized, and any further increase in amplitude will result in an error known as <a href="/wiki/Clipping_(signal_processing)" title="Clipping (signal processing)">clipping</a>. The amplitude of a digital signal can be represented in percent; full scale; or <a href="/wiki/DBFS" title="DBFS">decibels, full scale</a> (dBFS). </p><p>In analog systems, full scale may be defined by the maximum voltage available, or the maximum deflection (<b>full scale deflection</b> or <b>FSD</b>) or indication of an analog instrument such as a moving coil meter or <a href="/wiki/Galvanometer" title="Galvanometer">galvanometer</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Binary_representation">Binary representation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Full_scale&action=edit&section=1" title="Edit section: Binary representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since <a href="/wiki/Signed_number_representations#Two's_complement" title="Signed number representations">binary integer</a> representation range is asymmetrical, full scale is defined using the maximum positive value that can be represented.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> For example, <a href="/wiki/Audio_bit_depth" title="Audio bit depth">16-bit PCM audio</a> is centered on the value 0, and can contain values from −32,768 to +32,767. A signal is at full-scale if it reaches from −32,767 to +32,767. (This means that −32,768, the lowest possible value, slightly <i>exceeds</i> full-scale.) </p><p>Signal processing in <a href="/wiki/Digital_audio_workstation" title="Digital audio workstation">digital audio workstations</a> often uses <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating-point arithmetic</a>, which can include values past full-scale, to avoid clipping in intermediate processing stages. In a <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating-point</a> representation, a full-scale signal is typically defined to reach from −1.0 to +1.0.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Processing">Processing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Full_scale&action=edit&section=2" title="Edit section: Processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The signal passes through an <a href="/wiki/Anti-aliasing_filter" title="Anti-aliasing filter">anti-aliasing</a>, <a href="/wiki/Sample_rate_conversion" class="mw-redirect" title="Sample rate conversion">resampling</a>, or <a href="/wiki/Reconstruction_filter" title="Reconstruction filter">reconstruction filter</a>, which may increase peak amplitude slightly due to <a href="/wiki/Ringing_artifacts" title="Ringing artifacts">ringing</a>. </p><p>It is possible for the <i>analog</i> signal <i>represented by</i> the digital data to exceed digital full scale even if the digital data does not, and vice versa. Converting to the analog domain, there is no clipping problem as long as the analog circuitry in the <a href="/wiki/Digital-to-analog_converter" title="Digital-to-analog converter">digital-to-analog converter</a> is well designed. </p><p>If a full-scale analog signal is converted to digital with sufficient sampling frequency, and then <a href="/wiki/Signal_reconstruction" title="Signal reconstruction">reconstructed</a>, the <a href="/wiki/Nyquist_theorem" class="mw-redirect" title="Nyquist theorem">Nyquist theorem</a> guarantees that there will be no problem in the analog domain due to "peak" issues because the restored analog signal will be an exact copy of the original analog signal. (However, if the signal is <a href="/wiki/Audio_normalization" title="Audio normalization">normalized</a> in the digital domain, it may contain "intersample peaks" which exceed full scale after analog reconstruction.)<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Full_scale&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.aes.org/publications/standards/search.cfm?docID=21">"AES Standard » AES17-2015: AES standard method for digital audio engineering - Measurement of digital audio equipment"</a>. <i>www.aes.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-04-29</span></span>. <q>amplitude of a 997-Hz sine wave whose positive peak value reaches the positive digital full scale, leaving the negative maximum code unused. NOTE In 2's-complement representation, the negative peak is 1 LSB away from the negative maximum code.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.aes.org&rft.atitle=AES+Standard+%C2%BB+AES17-2015%3A+AES+standard+method+for+digital+audio+engineering+-+Measurement+of+digital+audio+equipment&rft_id=http%3A%2F%2Fwww.aes.org%2Fpublications%2Fstandards%2Fsearch.cfm%3FdocID%3D21&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFull+scale" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sis.se/api/document/preview/571704/">"IEC 61606-3:2008 Audio and audiovisual equipment - Digital audio parts - Basic measurement methods of audio characteristics - Part 3: Professional use"</a>. <i>International Electrotechnical Commission</i>. 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-07-27</span></span>. <q>amplitude of a 997 Hz sinusoid whose peak positive sample just reaches positive digital full-scale (in 2's-complement a binary value of 0111…1111 to make up the word length) and whose peak negative sample just reaches a value one away from negative digital full-scale (1000…0001 to make up the word length) leaving the maximum negative code (1000…0000) unused</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=International+Electrotechnical+Commission&rft.atitle=IEC+61606-3%3A2008+Audio+and+audiovisual+equipment+-+Digital+audio+parts+-+Basic+measurement+methods+of+audio+characteristics+-+Part+3%3A+Professional+use&rft.date=2008&rft_id=https%3A%2F%2Fwww.sis.se%2Fapi%2Fdocument%2Fpreview%2F571704%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFull+scale" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-mmsp.ece.mcgill.ca/Documents/AudioFormats/WAVE/WAVE.html">"Wave File Specifications"</a>. <i>McGill University Telecommunications & Signal Processing Laboratory</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-05-03</span></span>. <q>For float data, full scale is 1.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=McGill+University+Telecommunications+%26+Signal+Processing+Laboratory&rft.atitle=Wave+File+Specifications&rft_id=http%3A%2F%2Fwww-mmsp.ece.mcgill.ca%2FDocuments%2FAudioFormats%2FWAVE%2FWAVE.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFull+scale" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://rps.org/media/kq1pv42g/audition_user_guide.pdf">"Adobe Audition User Guide"</a> <span class="cs1-format">(PDF)</span>. <q>32-bit 0.24 normalized float (type 3 – 32-bit) is the standard floating point format for type 3 .wav files. Values are normalized to the range +/-1.0</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Adobe+Audition+User+Guide&rft_id=https%3A%2F%2Frps.org%2Fmedia%2Fkq1pv42g%2Faudition_user_guide.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFull+scale" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNielsenLund" class="citation web cs1">Nielsen, Søren H.; Lund, Thomas. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190502034621/https://service.tcgroup.tc/media/Level_paper_AES109%281%29.pdf">"0dBFS+ Levels in Digital Mastering"</a> <span class="cs1-format">(PDF)</span>. <i>TC Electronic A/S</i>. Denmark. Archived from <a rel="nofollow" class="external text" href="https://service.tcgroup.tc/media/Level_paper_AES109%281%29.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2019-05-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-07-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=TC+Electronic+A%2FS&rft.atitle=0dBFS%2B+Levels+in+Digital+Mastering&rft.aulast=Nielsen&rft.aufirst=S%C3%B8ren+H.&rft.au=Lund%2C+Thomas&rft_id=https%3A%2F%2Fservice.tcgroup.tc%2Fmedia%2FLevel_paper_AES109%25281%2529.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFull+scale" class="Z3988"></span></span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Full_scale&oldid=1223788633">https://en.wikipedia.org/w/index.php?title=Full_scale&oldid=1223788633</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Digital_signal_processing" title="Category:Digital signal processing">Digital signal processing</a></li><li><a href="/wiki/Category:Digital_audio" title="Category:Digital audio">Digital audio</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 14 May 2024, at 10:50<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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