Editing Sampling (signal processing) (section)

=== Audio sampling ===
[[Digital audio]] uses [[pulse-code modulation]] (PCM) and digital signals for sound reproduction. This includes analog-to-digital conversion (ADC), digital-to-analog conversion (DAC), storage, and transmission. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. While modern systems can be quite subtle in their methods, the primary usefulness of a digital system is the ability to store, retrieve and transmit signals without any loss of quality.

When it is necessary to capture audio covering the entire 20–20,000&nbsp;Hz range of [[auditory system|human hearing]]<ref>
{{cite web
 | url=https://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml
 | title=Frequency range of human hearing
 | first1=Christoper
 | last1=D'Ambrose
 | year=2003
 | first2=Rizwan
 | last2=Choudhary
 | website=The Physics Factbook
 | editor-last=Elert
 | editor-first=Glenn
 | accessdate=2022-01-22
}}</ref> such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44.1&nbsp;kHz ([[Compact Disc Digital Audio|CD]]), 48&nbsp;kHz, 88.2&nbsp;kHz, or 96&nbsp;kHz.<ref>{{cite book |url=https://books.google.com/books?id=WzYm1hGnCn4C&pg=PT200 |pages=200, 446 |last=Self |first=Douglas |title=Audio Engineering Explained |publisher=Taylor & Francis US |year=2012 |isbn=978-0240812731}}</ref> The approximately double-rate requirement is a consequence of the [[Nyquist theorem]]. Sampling rates higher than about 50&nbsp;kHz to 60&nbsp;kHz cannot supply more usable information for human listeners. Early [[professional audio]] equipment manufacturers chose sampling rates in the region of 40 to 50&nbsp;kHz for this reason.

There has been an industry trend towards sampling rates well beyond the basic requirements: such as 96&nbsp;kHz and even 192&nbsp;kHz<ref>{{cite web|url=http://www.digitalprosound.com/Htm/SoapBox/soap2_Apogee.htm |title=Digital Pro Sound |access-date=8 January 2014}}</ref> Even though [[Ultrasound|ultrasonic]] frequencies are inaudible to humans, recording and mixing at higher sampling rates is effective in eliminating the distortion that can be caused by [[Aliasing#Folding|foldback aliasing]]. Conversely, ultrasonic sounds may interact with and modulate the audible part of the frequency spectrum ([[intermodulation distortion]]), ''degrading'' the fidelity.<ref>{{cite journal|last=Colletti|first=Justin|date=February 4, 2013|title=The Science of Sample Rates (When Higher Is Better—And When It Isn't)|url=https://sonicscoop.com/2016/02/19/the-science-of-sample-rates-when-higher-is-better-and-when-it-isnt/?singlepage=1|journal=Trust Me I'm a Scientist|access-date=February 6, 2013|quote=in many cases, we can hear the sound of higher sample rates not because they are more transparent, but because they are less so. They can actually introduce unintended distortion in the audible spectrum}}</ref> One advantage of higher sampling rates is that they can relax the low-pass filter design requirements for [[analog-to-digital converter|ADCs]] and [[digital-to-analog converter|DACs]], but with modern oversampling [[Delta-sigma modulation|delta-sigma-converters]] this advantage is less important.

The [[Audio Engineering Society]] recommends 48&nbsp;kHz sampling rate for most applications but gives recognition to 44.1&nbsp;kHz for CD and other consumer uses, 32&nbsp;kHz for transmission-related applications, and 96&nbsp;kHz for higher bandwidth or relaxed [[anti-aliasing filter]]ing.<ref name=AES5>{{citation |url=http://www.aes.org/publications/standards/search.cfm?docID=14 |title=AES5-2008: AES recommended practice for professional digital audio – Preferred sampling frequencies for applications employing pulse-code modulation |publisher=Audio Engineering Society |year=2008 |access-date=2010-01-18}}</ref> Both Lavry Engineering and J. Robert Stuart state that the ideal sampling rate would be about 60&nbsp;kHz, but since this is not a standard frequency, recommend 88.2 or 96&nbsp;kHz for recording purposes.<ref>{{Cite web|url=http://www.lavryengineering.com/pdfs/lavry-white-paper-the_optimal_sample_rate_for_quality_audio.pdf|title=The Optimal Sample Rate for Quality Audio|last=Lavry|first=Dan|date=May 3, 2012|website=Lavry Engineering Inc.|quote=Although 60&nbsp;KHz would be closer to the ideal; given the existing standards, 88.2&nbsp;KHz and 96&nbsp;KHz are closest to the optimal sample rate.}}</ref><ref>{{Cite web|url=https://www.gearslutz.com/board/showpost.php?p=7883017&postcount=15&s=b05e50b41d1789054724882582d8351b|title=The Optimal Sample Rate for Quality Audio|last=Lavry|first=Dan|website=Gearslutz|language=en|access-date=2018-11-10|quote=I am trying to accommodate all ears, and there are reports of few people that can actually hear slightly above 20KHz. I do think that 48&nbsp;KHz is pretty good compromise, but 88.2 or 96&nbsp;KHz yields some additional margin.}}</ref><ref>{{Cite web|url=https://www.gearslutz.com/board/showpost.php?p=1234224&postcount=74|title=To mix at 96k or not?|last=Lavry|first=Dan|website=Gearslutz|language=en|access-date=2018-11-10|quote=Nowdays [sic] there are a number of good designers and ear people that find 60-70KHz sample rate to be the optimal rate for the ear. It is fast enough to include what we can hear, yet slow enough to do it pretty accurately.}}</ref><ref>{{Cite book|title=Coding High Quality Digital Audio|last=Stuart|first=J. Robert|date=1998|quote=both psychoacoustic analysis and experience tell us that the minimum rectangular channel necessary to ensure transparency uses linear PCM with 18.2-bit samples at 58&nbsp;kHz. ... there are strong arguments for maintaining integer relationships with existing sampling rates – which suggests that 88.2&nbsp;kHz or 96&nbsp;kHz should be adopted.|citeseerx = 10.1.1.501.6731}}</ref>

A more complete list of common audio sample rates is:

{| class="wikitable"
|-
 ! Sampling rate
 ! Use
|-
|5,512.5&nbsp;Hz
|Supported in [[Adobe Flash|Flash]].{{Cite web|url=https://open-flash.github.io/mirrors/swf-spec-19.pdf}}
|-
 | 8,000&nbsp;Hz
 | [[Telephone]] and encrypted [[walkie-talkie]], [[wireless intercom]] and [[wireless microphone]] transmission; adequate for human speech but without [[sibilance]] (''ess'' sounds like ''eff'' ({{IPAslink|s}}, {{IPAslink|f}})).
|-
 | 11,025&nbsp;Hz
 | One quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses.{{Citation needed|date=January 2011}}
|-
 | 16,000&nbsp;Hz
 | [[Wideband]] frequency extension over standard [[telephone]] [[narrowband]] 8,000&nbsp;Hz. Used in most modern [[VoIP]] and [[VVoIP]] communication products.<ref>{{Cite web|url=http://www.voipsupply.com/cisco-hd-voice|title = Cisco VoIP Phones, Networking and Accessories - VoIP Supply}}</ref>{{unreliable source?|date=September 2013}}
|-
 | 22,050&nbsp;Hz
 | One half the sampling rate of audio CDs; used for lower-quality PCM and MPEG audio and for audio analysis of low frequency energy. Suitable for digitizing early 20th century audio formats such as [[78 rpm|78s]] and [[AM Broadcasting|AM Radio]].<ref>{{cite web|url=http://www.restoring78s.co.uk/Procedure%20Part%201.htm |title=The restoration procedure – part 1 |publisher=Restoring78s.co.uk |access-date=2011-01-18|archive-url=https://web.archive.org/web/20090914133005/http://www.restoring78s.co.uk/Procedure%20Part%201.htm|archive-date=2009-09-14|quote=For most records a sample rate of 22050 in stereo is adequate. An exception is likely to be recordings made in the second half of the century, which may need a sample rate of 44100.}}</ref>
|-
 | 32,000&nbsp;Hz
 | [[miniDV]] digital video [[camcorder]], video tapes with extra channels of audio (e.g. [[DVCAM]] with four channels of audio), [[Digital Audio Tape|DAT]] (LP mode), Germany's [[:de:Digitales Satellitenradio|Digitales Satellitenradio]], [[NICAM]] digital audio, used alongside analogue television sound in some countries. High-quality digital [[wireless microphone]]s.<ref>{{cite web |url=http://www.zaxcom.com/transmitters.htm |title=Zaxcom digital wireless transmitters |publisher=Zaxcom.com |access-date=2011-01-18 |url-status=dead |archive-url=https://web.archive.org/web/20110209050359/http://zaxcom.com/transmitters.htm |archive-date=2011-02-09 }}</ref> Suitable for digitizing [[FM broadcasting|FM radio]].{{Citation needed|date=September 2011}}
|-
 | 37,800&nbsp;Hz
 | [[CD-ROM#CD-ROM XA extension|CD-XA audio]]
|-
 | 44,055.9&nbsp;Hz
 | Used by digital audio locked to [[NTSC]] ''color'' video signals (3 samples per line, 245 lines per field, 59.94 fields per second = 29.97 [[frames per second]]).
|-
 | [[44,100&nbsp;Hz]]
 | [[Audio CD]], also most commonly used with [[MPEG-1]] audio ([[VCD]], [[SVCD]], [[MP3]]). Originally chosen by [[Sony]] because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC ''monochrome'' video recorder) and cover the 20&nbsp;kHz bandwidth thought necessary to match professional analog recording equipment of the time. A [[PCM adaptor]] would fit digital audio samples into the analog video channel of, for example, [[PAL]] video tapes using 3 samples per line, 588 lines per frame, 25 frames per second.
|-
 | 47,250&nbsp;Hz
 | world's first commercial [[Pulse-code modulation|PCM]] sound recorder by [[Nippon Columbia]] (Denon)
|-
 | [[48,000&nbsp;Hz]]
 | The standard audio sampling rate used by professional digital video equipment such as tape recorders, video servers, vision mixers and so on. This rate was chosen because it could reconstruct frequencies up to 22&nbsp;kHz and work with 29.97&nbsp;frames per second NTSC video – as well as 25&nbsp;frame/s, 30&nbsp;frame/s and 24&nbsp;frame/s systems. With 29.97&nbsp;frame/s systems it is necessary to handle 1601.6 audio samples per frame delivering an integer number of audio samples only every fifth video frame.<ref name=AES5/> Also used for sound with consumer video formats like DV, [[digital TV]], [[DVD]], and films. The professional [[serial digital interface]] (SDI) and High-definition Serial Digital Interface (HD-SDI) used to connect broadcast television equipment together uses this audio sampling frequency. Most professional audio gear uses 48&nbsp;kHz sampling, including [[mixing console]]s, and [[digital recording]] devices.
|-
 | 50,000&nbsp;Hz
 | First commercial digital audio recorders from the late 70s from [[3M]] and [[Soundstream]].
|-
 | 50,400&nbsp;Hz
 | Sampling rate used by the [[X-80|Mitsubishi X-80]] digital audio recorder.
|-
 | 64,000&nbsp;Hz
 | Uncommonly used, but supported by some hardware<ref>{{Cite web|url=http://www.rme-audio.de/en/products/hdsp_9632.php|title=RME: Hammerfall DSP 9632|website=www.rme-audio.de|access-date=2018-12-18|quote=Supported sample frequencies: Internally 32, 44.1, 48, 64, 88.2, 96, 176.4, 192&nbsp;kHz.}}</ref><ref>{{Cite web|url=https://www.pioneer-audiovisual.eu/uk/products/sx-s30dab|title=SX-S30DAB {{!}} Pioneer|website=www.pioneer-audiovisual.eu|access-date=2018-12-18|quote=Supported sampling rates: 44.1&nbsp;kHz, 48&nbsp;kHz, 64&nbsp;kHz, 88.2&nbsp;kHz, 96&nbsp;kHz, 176.4&nbsp;kHz, 192&nbsp;kHz}}</ref> and software.<ref>{{Cite web|url=https://steinberg.help/wavelab_pro/v9.5/en/wavelab/topics/master_section/master_section_customize_sample_rate_menu_dialog_r.html|title=Customize Sample Rate Menu|last1=Cristina Bachmann|first1=Heiko Bischoff|last2=Schütte|first2=Benjamin|website=Steinberg WaveLab Pro|language=en-US|access-date=2018-12-18|quote=Common Sample Rates: 64 000 Hz}}</ref><ref>{{Cite web|url=https://getsatisfaction.com/m-audio/topics/m-track-2x2m-cubase-pro-9-can-t-change-sample-rate|title=M Track 2x2M Cubase Pro 9 can ́t change Sample Rate|website=M-Audio|language=en-US|access-date=2018-12-18|quote=[Screenshot of Cubase]}}</ref>
|-
 | 88,200&nbsp;Hz
 | Sampling rate used by some professional recording equipment when the destination is CD (multiples of 44,100&nbsp;Hz). Some pro audio gear uses (or is able to select) 88.2&nbsp;kHz sampling, including mixers, EQs, compressors, reverb, crossovers, and recording devices.
|-
 | 96,000&nbsp;Hz
 | [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, [[HD DVD]] (High-Definition DVD) audio tracks. Some professional recording and production equipment is able to select 96&nbsp;kHz sampling. This sampling frequency is twice the 48&nbsp;kHz standard commonly used with audio on professional equipment.
|-
 | 176,400&nbsp;Hz
 | Sampling rate used by [[HDCD]] recorders and other professional applications for CD production. Four times the frequency of 44.1&nbsp;kHz.
|-
 | 192,000&nbsp;Hz
 | [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, and [[HD DVD]] (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software. This sampling frequency is four times the 48&nbsp;kHz standard commonly used with audio on professional video equipment.
|-
 | 352,800&nbsp;Hz
 | [[Digital eXtreme Definition]], used for recording and editing [[Super Audio CD]]s, as 1-bit [[Direct Stream Digital|Direct Stream Digital (DSD)]] is not suited for editing. 8 times the frequency of 44.1&nbsp;kHz.
|-
|384,000 Hz
|Maximum sample rate available in common software.{{cn|date=January 2025}}
|-
 | 2,822,400&nbsp;Hz
 | [[Super Audio CD|SACD]], 1-bit [[delta-sigma modulation]] process known as [[Direct Stream Digital]], co-developed by [[Sony]] and [[Philips]].
|-
 | 5,644,800&nbsp;Hz
 | Double-Rate DSD, 1-bit [[Direct Stream Digital]] at 2× the rate of the SACD. Used in some professional DSD recorders.
|-
 | 11,289,600&nbsp;Hz
 | Quad-Rate DSD, 1-bit [[Direct Stream Digital]] at 4× the rate of the SACD. Used in some uncommon professional DSD recorders.
|-
 | 22,579,200&nbsp;Hz
 | Octuple-Rate DSD, 1-bit [[Direct Stream Digital]] at 8× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD512.
|-
 | 45,158,400&nbsp;Hz
 | Sexdecuple-Rate DSD, 1-bit [[Direct Stream Digital]] at 16× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD1024.{{efn-ua|Even higher DSD sampling rates exist, but the benefits of those are likely imperceptible, and the size of those files would be humongous.}}
|}

==== Bit depth ====
{{See also|Audio bit depth}}

Audio is typically recorded at 8-, 16-, and 24-bit depth; which yield a theoretical maximum [[signal-to-quantization-noise ratio]] (SQNR) for a pure [[sine wave]] of, approximately; 49.93&nbsp;[[Decibel|dB]], 98.09&nbsp;dB, and 122.17&nbsp;dB.<ref>{{cite web|url=http://www.analog.com/static/imported-files/tutorials/MT-001.pdf |title=MT-001: Taking the Mystery out of the Infamous Formula, "SNR=6.02N + 1.76dB," and Why You Should Care}}</ref> CD quality audio uses 16-bit samples. [[Thermal noise]] limits the true number of bits that can be used in quantization. Few analog systems have [[Signal-to-noise ratio|signal to noise ratios]] (SNR) exceeding 120&nbsp;dB. However, [[digital signal processing]] operations can have very high dynamic range, consequently it is common to perform mixing and mastering operations at 32-bit precision and then convert to 16- or 24-bit for distribution.

==== Speech sampling ====
Speech signals, i.e., signals intended to carry only human [[Speech communication|speech]], can usually be sampled at a much lower rate. For most [[phoneme]]s, almost all of the energy is contained in the 100&nbsp;Hz – 4&nbsp;kHz range, allowing a sampling rate of 8&nbsp;kHz. This is the sampling rate used by nearly all [[telephony]] systems, which use the [[G.711]] sampling and quantization specifications.{{Citation needed|reason=References are needed for frequency range of human voice, and use of G.711|date=May 2018}}