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[[File:4-bit-linear-PCM.svg|thumb|An analogue signal (in red) encoded to 4-bit PCM digital samples (in blue); the bit depth is 4, so each sample's amplitude is one of 16 possible values.]]
 
In [[digital audio]] using [[pulse-code modulation]] (PCM), '''bit depth''' is the number of [[bit]]s of information in each [[Sampling (signal processing)|sample]], and it directly corresponds to the '''resolution''' of each sample. Examples of bit depth include [[Compact Disc Digital Audio]], which uses 16 bits per sample, and [[DVD-Audio]] and [[Blu-ray Disc]] which can support up to 24 bits per sample.
 
In basic implementations, variations in bit depth primarily affect the noise level from [[quantization error]]—thus the [[signal-to-noise ratio]] (SNR) and [[dynamic range]]. However, techniques such as [[dither]]ing, [[noise shaping]] and [[oversampling]] mitigate these effects without changing the bit depth. Bit depth also affects [[bit rate]] and file size.
 
Bit depth is only meaningful in reference to a PCM [[digital signal]]. Non-PCM formats, such as [[lossy compression]] formats like [[MP3]], [[Advanced Audio Coding|AAC]] and [[Vorbis]], do not have associated bit depths. For example, in MP3, quantization is performed on PCM samples that have been transformed into the [[frequency domain]].
 
== Binary resolution ==
A PCM signal is a sequence of digital audio samples containing the data providing the necessary information to [[Signal reconstruction|reconstruct]] the original [[analog signal]]. Each sample represents the [[amplitude]] of the signal at a specific point in time, and the samples are uniformly spaced in time. The amplitude is the only information explicitly stored in the sample, and it is typically stored as either an [[integer]] or a [[floating point]] number, encoded as a [[binary number]] with a fixed number of digits: the sample's ''bit depth''.
 
The resolution of binary integers increases [[Exponentiation|exponentially]] as the word length increases. Adding one bit doubles the resolution, adding two quadruples it and so on. The number of possible values that can be represented by an integer bit depth can be calculated by using [[Power of two|2<sup>''n''</sup>]], where ''n'' is the bit depth.<ref name="Understanding Audio">Thompson, Dan (2005). ''Understanding Audio''. Berklee Press. ISBN 978-0-634-00959-4.</ref> Thus, a [[16-bit]] system has a resolution of 65,536 (2<sup>16</sup>) possible values.
 
PCM audio data is typically stored as [[Signedness|signed]] numbers in [[two's complement]] format.<ref name="Julius PCM">{{cite web | url=https://ccrma.stanford.edu/~jos/mdft/Pulse_Code_Modulation_PCM.html | title=Pulse Code Modulation (PCM) | author=Smith, Julius | year=2007 | work=Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, Second Edition, online book | accessdate= 22 October 2012}}</ref>
 
=== Floating point ===
Many audio [[file format]]s and [[digital audio workstation]]s (DAWs) now support PCM formats with samples represented by [[floating point]] numbers. Both the [[WAV]] file format and the [[Audio Interchange File Format|AIFF]] file format support floating point PCM<ref name="waveref">{{cite web |url=http://www-mmsp.ece.mcgill.ca/documents/AudioFormats/WAVE/WAVE.html |title=Audio File Format Specifications, WAVE Specifications |author=Kabal, Peter |date=3 January 2011 |publisher=McGill University |accessdate=10 August 2013}}</ref><ref name="aiffref">{{cite web |url=http://www-mmsp.ece.mcgill.ca/Documents/AudioFormats/AIFF/AIFF.html |title=Audio File Format Specifications, AIFF / AIFF-C Specifications |author=Kabal, Peter |date=3 January 2011 |publisher=McGill University |accessdate=10 August 2013}}</ref> and major DAWs such as [[Pro Tools]], [[Reason (software)|Reason]], [[FL Studio]], and [[Ableton Live]] support varied floating point processing capabilities.<ref name="ptnativefloat">{{cite book |url=http://books.google.com/books?id=0WEKAAAAQBAJ&lpg=PA239&pg=PA247#v=onepage&q&f=false |title=Pro Tools 10 Advanced Music Production Techniques, pg. 247 |author=Campbell, Robert |year=2013 |publisher=Cengage Learning |accessdate=12 August 2013}}</ref><ref name="protools10float">{{cite web |url=http://www.soundonsound.com/sos/mar12/articles/pt-10.htm |title=Avid Pro Tools 10 |author=Wherry, Mark |date=March 2012 |publisher=Sound On Sound |accessdate=10 August 2013}}</ref><ref name="reasonfloat">{{cite web |url=http://www.soundonsound.com/sos/oct05/articles/reasontechnique.htm |title=Reason Mixing Masterclass |author=Price, Simon |date=October 2005 |publisher=Sound On Sound |accessdate=10 August 2013}}</ref><ref name="live9manual">{{cite web | url=https://www.ableton.com/en/manual/mixing/ | title=Ableton Reference Manual Version 9, 15. Mixing | publisher=Ableton | year=2013 | accessdate=26 August 2013}}</ref>
 
Unlike integers, whose bit pattern is a single series of bits, a floating point number is instead composed of separate fields whose mathematical relation forms a number. The most common standard is [[IEEE floating point]] which is composed of three bit patterns: a [[sign bit]] which represents whether the number is positive or negative, an exponent and a [[Significand|mantissa]] which is raised by the exponent. The mantissa is expressed as a [[Binary number#Fractions|binary fraction]] in IEEE base two floating point formats.<ref name="dspguide4">{{cite web |url=http://www.dspguide.com/ch4/3.htm |title=The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 4 – DSP Software / Floating Point (Real Numbers) |author=Smith, Steven |year=1997-1998 |website=www.dspguide.com |accessdate=10 August 2013}}</ref>
 
== Quantization ==
The bit depth limits the [[signal-to-noise ratio]] (SNR) of the reconstructed signal to a maximum level determined by [[Quantization (signal processing)|quantization]] error. The bit depth has no impact on the [[frequency response]], which is constrained by the [[sample rate]].
 
Quantization noise is a [[Model (abstract)|model]] of quantization error introduced by the [[Sampling (signal processing)|sampling]] process during [[Analog-to-digital converter|analog-to-digital conversion]] (ADC). It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is [[Nonlinear system|nonlinear]] and signal-dependent.
 
[[Image:Least significant bit.svg|thumb|280px|right|An [[8-bit]] binary number of the base ten value 149 with the LSB highlighted.]]
 
In an ideal ADC, where the quantization error is uniformly distributed between <math>\scriptstyle{\pm \frac{1}{2}}</math> [[least significant bit]] (LSB) and where the signal has a uniform distribution covering all quantization levels, the [[signal-to-quantization-noise ratio]] (SQNR) can be calculated from
 
:<math>\mathrm{SQNR} = 20 \log_{10}(2^Q) \approx 6.02 \cdot Q\ \mathrm{dB} \,\!</math>
 
where Q is the number of quantization bits and the result is measured in [[decibel]]s (dB).<ref>See [[Signal-to-noise ratio#Fixed point]])</ref><ref>{{cite web |url=http://www.analog.com/static/imported-files/tutorials/MT-001.pdf |title=Taking the Mystery out of the Infamous Formula, "SNR = 6.02N + 1.76dB," and Why You Should Care |author= Walt Kester |publisher=[[Analog Devices]] |year=2007 |accessdate=26 July 2011| archiveurl= http://web.archive.org/web/20110616182255/http://www.analog.com/static/imported-files/tutorials/MT-001.pdf| archivedate= 16 June 2011 <!--DASHBot-->| deadurl= no}}</ref>
 
[[24-bit]] digital audio has a theoretical maximum SNR of 144&nbsp;dB, compared to 96&nbsp;dB for 16-bit; however, {{asof|2007|lc=on}} digital audio converter technology is limited to a SNR of about 124&nbsp;dB (21-bit)<ref>{{cite web |url=http://focus.ti.com/docs/prod/folders/print/pcm4222.html |title=PCM4222 |accessdate=21 April 2011}}</ref> because of real-world limitations in [[integrated circuit]] design. Still, this approximately matches the performance of the human [[auditory system]].<ref>{{cite web |url=http://media.paisley.ac.uk/~campbell/AASP/Aspects%20of%20Human%20Hearing.PDF |title=Aspects of Human Hearing |author=D. R. Campbell |quote=The dynamic range of human hearing is [approximately] 120&nbsp;dB |accessdate=21 April 2011}}</ref><ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/sound/earsens.html#c2 |quote=The practical dynamic range could be said to be from the threshold of hearing to the threshold of pain [130&nbsp;dB] |title=Sensitivity of Human Ear |accessdate=21 April 2011| archiveurl= http://web.archive.org/web/20110604105752/http://hyperphysics.phy-astr.gsu.edu/hbase/sound/earsens.html| archivedate= 4 June 2011 <!--DASHBot-->| deadurl= no}}</ref>
 
{| class="wikitable"
|+ Signal-to-noise ratio and resolution of bit depths
! # bits !! SNR !! Possible integer values !! Base ten signed range
|-
!4
| 24.08 dB || 16 || −8 to +7
|-
!8
| 48.16 dB || 256 || −128 to +127
|-
!11<ref>This is the bit depth that the [[Raspberry Pi]] uses when driving the [[Pulse-width modulation|pulse-width modulator]] of its BCM2835 chip</ref>
| 66.22 dB || 2048 || −1024 to +1023
|-
!16
| 96.33 dB || 65,536 || −32,768 to +32,767
|-
!20
| 120.41 dB || 1,048,576 || −524,288 to +524,287
|-
!24
| 144.49 dB || 16,777,216 || −8,388,608 to +8,388,607
|-
!32
| 192.66 dB || 4,294,967,296 || −2,147,483,648 to +2,147,483,647
|-
!48
| 288.99 dB || 281,474,976,710,656 || −140,737,488,355,328 to +140,737,488,355,327
|-
!64
| 385.32 dB || 18,446,744,073,709,551,616 || −9,223,372,036,854,775,808 to +9,223,372,036,854,775,807
|}
 
The resolution of floating point samples is less straightforward than integer samples, but the benefit comes in the increased accuracy of low values. In floating point representation, the space between any two adjacent values is of the same proportion as the space between any other two adjacent values, whereas in an integer representation, the space between adjacent values gets larger in proportion to low-level signals. This greatly increases the SNR because the accuracy of a high-level signal will be the same as the accuracy of an identical signal at a lower level.<ref name="dspguide28">{{cite web |url=http://www.dspguide.com/ch28/4.htm |title=The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 28 – Digital Signal Processors / Fixed versus Floating Point |author=Smith, Steven |year=1997–1998 |website=www.dspguide.com |accessdate=10 August 2013}}</ref>
 
The trade-off between floating point and integers is that the space between large floating point values is greater than the space between large integer values of the same bit depth. Rounding a large floating point number results in a greater error than rounding a small floating point number whereas rounding an integer number will always result in the same level of error. In other words, integers have round-off that is uniform, always rounding the LSB to 0 or 1, and floating point has SNR that is uniform, the quantization noise level is always of a certain proportion to the signal level.<ref name="dspguide28" /> A floating point noise floor will rise as the signal rises and fall as the signal falls, resulting in audible variance if the bit depth is low enough.<ref name="48forproaudio">{{cite web |url=http://www.jamminpower.com/PDF/48-bit%20Audio.pdf |title=48-Bit Integer Processing Beats 32-Bit Floating-Point for Professional Audio Applications |author=Moorer, James |date=September 1999 |website=www.jamminpower.com |accessdate=12 August 2013}}</ref>
 
=== Audio processing ===
Most processing operations on digital audio involve requantization of samples, and thus introduce additional rounding error analogous to the original quantization error introduced during analog to digital conversion. To prevent rounding error larger than the implicit error during ADC, calculations during processing must be performed at higher precisions than the input samples.<ref name="wordrelation">{{cite web| url=http://www.analog.com/en/content/relationship_data_word_size_dynamic_range/fca.html |title=THE RELATIONSHIP OF DATA WORD SIZE TO DYNAMIC RANGE AND SIGNAL QUALITY IN DIGITAL AUDIO PROCESSING APPLICATIONS |author=Tomarakos, John |publisher=Analog Systems |website=www.analog.com |accessdate=16 August 2013 }}</ref>
 
[[Digital signal processing]] (DSP) operations can be performed in either [[Fixed-point arithmetic|fixed point]] or floating point precision. In either case, the precision of each operation is determined by the precision of the hardware operations used to perform each step of the processing and not the resolution of the input data. For example, on [[x86]] processors, floating point operations are performed at 32- or 64-bit precision and fixed point operations at 16-, 32- or 64-bit resolution. Consequently, all processing performed on Intel-based hardware will be performed at 16-, 32- or 64-bit integer precision, or 32- or 64-bit floating point precision regardless of the source format. However, if memory is at a premium, software may still choose to output lower resolution 16- or 24-bit audio after higher precision processing.
 
Fixed point [[digital signal processor]]s often support unusual word sizes and precisions in order to support specific signal resolutions. For example, the [[Motorola 56000]] DSP chip uses 24-bit word sizes, 24-bit multipliers and 56-bit accumulators to perform [[multiply-accumulate operation]]s on two 24-bit samples without overflow or rounding.<ref>{{cite web|title=DSP56001A|url=http://cache.freescale.com/files/dsp/doc/inactive/DSP56001A.pdf|publisher=Freescale|accessdate=15 August 2013}}</ref> On devices that do not support large accumulators, fixed point operations may be implicitly rounded, reducing precision to below that of the input samples.
 
Errors compound through multiple stages of DSP at a rate that depends on the operations being performed. For uncorrelated processing steps on audio data without a DC offset, errors are assumed to be random with zero mean. Under this assumption, the standard deviation of the distribution represents the error signal, and quantization error scales with the square root of the number of operations.<ref>{{cite web|last=Smith|first=Steven|title=he Scientist and Engineer's Guide to Digital Signal Processing|url=http://www.dspguide.com/ch4/4.htm|work=Ch. 4|accessdate=19 August 2013}}</ref> High levels of precision are necessary for algorithms that involve repeated processing, such as [[convolution]].<ref name="wordrelation"/> High levels of precision are also necessary in recursive algorithms, such as [[infinite impulse response]] (IIR) filters.<ref>{{cite journal|last=Carletta|first=Joan|title=Determining Appropriate Precisions for Signals in Fixed-Point IIR Filters|journal=DAC|year=2003|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.1266&rep=rep1&type=pdf|accessdate=15 August 2013}}</ref> In the particular case of IIR filters, rounding error can degrade frequency response and cause instability.<ref name="wordrelation"/>
 
== Dither ==
{{main|Dither}}
The noise introduced by quantization error, including rounding errors and loss of precision introduced during audio processing, can be mitigated by adding a small amount of random noise, called [[dither]], to the signal before quantizing. Dithering eliminates the granularity of quantization error, giving very low distortion, but at the expense of a slightly raised [[noise floor]]. Measured using [[ITU-R 468 noise weighting]], this is about 66&nbsp;dB below [[alignment level]], or 84&nbsp;dB below digital [[full scale]], which is somewhat lower than the microphone noise level on most recordings, and hence of no consequence in 16-bit audio (see [[Programme level]] for more on this).
 
24-bit audio does not require dithering, as the noise level of the digital converter is always louder than the required level of any dither that might be applied. 24-bit audio could theoretically encode 144 dB of dynamic range, but no ADCs exist that can provide higher than ~125 dB.<ref>[http://skywired.net/blog/2011/09/choosing-high-performance-audio-adc/ Choosing a high-performance audio ADC] - "I went looking for the best dynamic range audio ADC I could find" and highest are 123 dB dynamic range</ref>
 
Dither can also be used to increase the effective dynamic range. The ''perceived'' dynamic range of 16-bit audio can be as high as 120 dB with noise-shaped [[dither]], taking advantage of the frequency response of the human ear.<ref>{{cite web |url=https://www.xiph.org/~xiphmont/demo/neil-young.html |title=24/192 Music Downloads ...and why they make no sense |last=Montgomery |first=Chris |authorlink=Chris Montgomery |date=March 25, 2012 |website=xiph.org |accessdate=26 May 2013 |quote=With use of shaped dither, which moves quantization noise energy into frequencies where it's harder to hear, the effective dynamic range of 16 bit audio reaches 120dB in practice, more than fifteen times deeper than the 96dB claim. 120dB is greater than the difference between a mosquito somewhere in the same room and a jackhammer a foot away.... or the difference between a deserted 'soundproof' room and a sound loud enough to cause hearing damage in seconds. 16 bits is enough to store all we can hear, and will be enough forever.}}</ref>
 
== Dynamic range ==
[[Dynamic range]] is the difference between the largest and smallest signal a system can record or reproduce. Without dither, the dynamic range correlates to the quantization noise floor. For example, 16-bit integer resolution allows for a dynamic range of about 96&nbsp;dB.
 
Using higher bit depths during [[Recording studio|studio recording]] accommodates greater dynamic range. If the signal's dynamic range is lower than that allowed by the bit depth, the recording has [[Headroom (audio signal processing)|headroom]], and the higher the bit depth, the more headroom that's available. This reduces the risk of [[Clipping (audio)|clipping]] without encountering quantization errors at low volumes.
 
With the proper application of dither, digital systems can reproduce signals with levels lower than their resolution would normally allow, extending the effective dynamic range beyond the limit imposed by the resolution.<ref>{{cite web |url=http://www.e2v.com/assets/media/files/documents/broadband-data-converters/doc0869B.pdf |title=Dithering in Analog-to-Digital Conversion |publisher=e2v Semiconductors |year=2007 |accessdate=26 July 2011}}</ref>
 
The use of techniques such as [[oversampling]] and [[noise shaping]] can further extend the dynamic range of sampled audio by moving quantization error out of the frequency band of interest.
 
=== Oversampling ===
{{Main|Oversampling}}
 
Oversampling is an alternative method to increase the dynamic range of PCM audio without changing the number of bits per sample.<ref>{{cite web|last=Kester|first=Walt|title=Oversampling Interpolating DACs|url=http://www.analog.com/static/imported-files/tutorials/MT-017.pdf|publisher=Analog Devices|accessdate=19 August 2013}}</ref> In oversampling, audio samples are acquired at a multiple of the desired sample rate. Because quantization error is assumed to be uniformly distributed with frequency, much of the quantization error is shifted to ultrasonic frequencies, and can be removed by the [[digital to analog converter]] during playback.
 
For an increase equivalent to ''n'' additional bits of resolution, a signal must be oversampled by
 
:<math> \mathrm{number\ of\ samples} = (2^n)^2 = 2^{2n}.</math>
 
For example, a 14-bit ADC can produce 16-bit 48&nbsp;kHz audio if operated at 16x oversampling, or 768&nbsp;kHz. Oversampled PCM therefore exchanges fewer bits per sample for more samples in order to obtain the same resolution.
 
=== Noise shaping ===
{{Main|Noise shaping}}
 
Oversampling a signal results in equal quantization noise per unit of bandwidth at all frequencies and a dynamic range that improves with only the square root of the oversampling ratio. Noise shaping is a technique that adds additional noise at higher frequencies which cancels out some error at lower frequencies, resulting in a larger increase in dynamic range when oversampling. For ''n''th-order noise shaping, the dynamic range of an oversampled signal is improved by an additional 6''n''&nbsp;dB relative to oversampling without noise shaping.<ref>{{cite web|title=B.1 First and Second-Order Noise Shaping Loops|url=http://www.iue.tuwien.ac.at/phd/schrom/node115.html|accessdate=19 August 2013}}</ref> For example, for a 20&nbsp;kHz analog audio sampled at 4x oversampling with second order noise shaping, the dynamic range is increased by 30&nbsp;dB. Therefore a 16-bit signal sampled at 176&nbsp;kHz would have equal resolution as a 21-bit signal sampled at 44.1&nbsp;kHz without noise shaping.
 
Noise shaping is commonly implemented with [[delta-sigma modulation]]. Using delta-sigma modulation, [[Super Audio CD]] obtains 120&nbsp;dB SNR at audio frequencies using 1-bit audio with 64x oversampling.
 
== Applications ==
Bit depth is a fundamental property of digital audio implementations and there are a variety of situations where it is a measurement.
 
{| class="wikitable"
|+ style="padding: 6px;" | Example applications and bits per sample
! style="padding: 6px; border-bottom: 3px solid darkgray;" | Application !! style="padding: 6px; border-bottom: 3px solid darkgray;" | Description !! style="padding: 6px; border-bottom: 3px solid darkgray;" | Audio format(s)
|-
! style="text-align: left; background: #f6f6f6;" | [[Compact Disc Digital Audio|CD-DA]] (Red Book)<ref name="cdda">{{cite web | url=http://www.sweetwater.com/sweetcare/articles/masterlink-what-red-book-cd/ | title=Sweetwater Knowledge Base, Masterlink: What is a "Red Book" CD? | publisher=Sweetwater | date=27 April 2007 | website=www.sweetwater.com | accessdate=25 August 2013}}</ref>
| Digital media || 16-bit [[Linear pulse-code modulation|LPCM]]
|-
! style="text-align: left; background: #f6f6f6;" | [[DVD-Audio]]<ref name="dvdaudio">{{cite web |url=http://web.archive.org/web/20120304060434/http://patches.sonic.com/pdf/white-papers/wp_dvd_audio.pdf |title=Understanding DVD-Audio |publisher=Sonic Solutions |format=PDF |accessdate=25 August 2013 }}</ref>
| Digital media || 16-, 20- and 24-bit LPCM<ref group=note>DVD-Audio also supports optional [[Meridian Lossless Packing]], a [[lossless compression]] scheme.</ref>
|-
! style="text-align: left; background: #f6f6f6;" | Super Audio CD<ref name="surround">{{cite web | url=http://www.extremetech.com/computing/48844-surround-sound/10 | title=Surround Sound, Page 10 | author=Shapiro, L. | publisher=ExtremeTech | date=2 July 2001 | accessdate=26 August 2013}}</ref>
| Digital media || 1-bit [[Direct Stream Digital]] ([[Pulse-density modulation|PDM]])
|-
! style="text-align: left; background: #f6f6f6;" | [[Blu-ray Disc#Audio|Blu-ray Disc audio]]<ref name="bluray">{{cite web| url=http://www.blu-raydisc.com/assets/Downloadablefile/BD-ROM-AV-WhitePaper_100423-17830.pdf | title=White paper Blu-ray Disc Format, 2.B Audio Visual Application Format Specifications for BD-ROM Version 2.4 |date=April 2010 | publisher = Blu-ray Disc Association | format=PDF | accessdate=25 August 2013}}</ref>
| Digital media || 16-, 20- and 24-bit LPCM and others<ref group=note>Blu-ray supports a variety of non-LPCM formats but all conform to some combination of 16, 20 and 24 bits per sample.</ref>
|- style="border-bottom: 2px solid darkgray;"
! style="text-align: left; background: #f6f6f6;"| [[DV]] audio<ref name="dvaudio">{{cite web | url=http://www.stanford.edu/~hbreit/CILECT/DV_Report.htm | title=DV – A SUCCESS STORY | author=Puhovski, Nenad |date=April 2000 | website=www.stanford.edu | accessdate=26 August 2013}}</ref>
| Digital media || 12-bit compressed PCM and 16-bit uncompressed PCM
|-
! style="text-align: left; background: #f6f6f6;" | [[ITU-T]] Recommendation [[G.711]]<ref name="g711">{{cite web | url=http://www.itu.int/rec/T-REC-G.711-198811-I/en | title=G.711 : Pulse code modulation (PCM) of voice frequencies | publisher=International Telecommunications Union | format=PDF | accessdate=25 August 2013}}</ref>
| Compression standard for [[telephony]] || 8-bit PCM with [[companding]]<ref group=note>ITU-T specifies the [[A-law algorithm|A-law]] and [[μ-law algorithm|μ-law]] companding algorithms, compressing down from 13 and 14 bits respectively.</ref>
|- style="border-bottom: 2px solid darkgray;"
! style="text-align: left; background: #f6f6f6;" | [[NICAM]]-1, NICAM-2 and NICAM-3<ref name="nicam">{{cite web | url=http://web.archive.org/web/20121108045757/http://downloads.bbc.co.uk/rd/pubs/reports/1978-26.pdf | title=DIGITAL SOUND SIGNALS: tests to compare the performance of five companding systems for high-quality sound signals | publisher=BBC Research Department |date=August 1978 | accessdate=26 August 2013}}</ref>
| Compression standards for [[broadcasting]] || 10-, 11- and 10-bit PCM respectively, with companding<ref group=note>NICAM systems 1, 2 and 3 compress down from 13, 14 and 14 bits respectively.</ref>
|-
! style="text-align: left; background: #f6f6f6;" | Pro Tools 11<ref name="ptdocs">{{cite web | url=http://avid.force.com/pkb/articles/en_US/User_Guide/Pro-Tools-11-Documentation | title=Pro Tools Documentation, Pro Tools Reference Guide | publisher=Avid | year=2013 | format=ZIP/PDF | accessdate=26 August 2013}}</ref>
| DAW by [[Avid Technology]] || 16- and 24-bit or 32-bit floating point sessions and 64-bit floating point [[Audio mixing (recorded music)|mixing]]
|-
! style="text-align: left; background: #f6f6f6;" | [[Logic Pro]] X<ref name="logicxguide">{{cite web | url=http://manuals.info.apple.com/en_US/logic_pro_x_user_guide.pdf | title=Logic Pro X - User Guide | publisher=Apple |date=January 2010 | format=PDF | accessdate=26 August 2013}}</ref>
| DAW by [[Apple Inc.]] || 16- and 24-bit projects
|-
! style="text-align: left; background: #f6f6f6;" | [[GarageBand]] '11 (version 6)<ref name="garageband">{{cite web | url=http://support.apple.com/kb/PH1873 | title=GarageBand '11: Set the audio resolution | publisher=Apple | date=13 March 2012 | accessdate=26 August 2013}}</ref>
| DAW by Apple Inc. || 16-bit default with 24-bit real instrument recording
|-
! style="text-align: left; background: #f6f6f6;" | Live 9<ref name="live9manual"/>
| DAW by [[Ableton]] || 32-bit floating point mixing
|- style="border-bottom: 2px solid darkgray;"
! style="text-align: left; background: #f6f6f6;" | Reason 7<ref name="reasonmanual">{{cite web | url=http://dl.propellerheads.se/Reason7/Manuals/Reason_7_Operation_Manual.pdf | title=Reason 7 Operation Manual | publisher=Propellerhead Software | year=2013 | format=PDF | accessdate=26 August 2013}}</ref>
| DAW by [[Propellerhead Software]] || 16-, 20- and 24-bit I/O, 32-bit floating point arithmetic and 64-bit summing
|}
 
== Bit rate and file size ==
Bit depth affects [[bit rate]] and file size. Bit rate refers to the amount of data, specifically bits, transmitted or received per second.
 
== See also ==
*[[Audio system measurements]]
*[[Color depth]]—corresponding concept for digital images
*[[Effective number of bits]]
 
== Notes ==
{{reflist|group=note}}
 
== References ==
{{Reflist}}
*{{cite book |title=Principles of Digital Audio |edition=4th |author=Ken C. Pohlmann |publisher=McGraw-Hill Professional |isbn=978-0-07-134819-5 |date=15 February 2000}}
 
[[Category:Digital audio]]

Revision as of 20:27, 29 December 2013

An analogue signal (in red) encoded to 4-bit PCM digital samples (in blue); the bit depth is 4, so each sample's amplitude is one of 16 possible values.

In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample.

In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range. However, techniques such as dithering, noise shaping and oversampling mitigate these effects without changing the bit depth. Bit depth also affects bit rate and file size.

Bit depth is only meaningful in reference to a PCM digital signal. Non-PCM formats, such as lossy compression formats like MP3, AAC and Vorbis, do not have associated bit depths. For example, in MP3, quantization is performed on PCM samples that have been transformed into the frequency domain.

Binary resolution

A PCM signal is a sequence of digital audio samples containing the data providing the necessary information to reconstruct the original analog signal. Each sample represents the amplitude of the signal at a specific point in time, and the samples are uniformly spaced in time. The amplitude is the only information explicitly stored in the sample, and it is typically stored as either an integer or a floating point number, encoded as a binary number with a fixed number of digits: the sample's bit depth.

The resolution of binary integers increases exponentially as the word length increases. Adding one bit doubles the resolution, adding two quadruples it and so on. The number of possible values that can be represented by an integer bit depth can be calculated by using 2n, where n is the bit depth.[1] Thus, a 16-bit system has a resolution of 65,536 (216) possible values.

PCM audio data is typically stored as signed numbers in two's complement format.[2]

Floating point

Many audio file formats and digital audio workstations (DAWs) now support PCM formats with samples represented by floating point numbers. Both the WAV file format and the AIFF file format support floating point PCM[3][4] and major DAWs such as Pro Tools, Reason, FL Studio, and Ableton Live support varied floating point processing capabilities.[5][6][7][8]

Unlike integers, whose bit pattern is a single series of bits, a floating point number is instead composed of separate fields whose mathematical relation forms a number. The most common standard is IEEE floating point which is composed of three bit patterns: a sign bit which represents whether the number is positive or negative, an exponent and a mantissa which is raised by the exponent. The mantissa is expressed as a binary fraction in IEEE base two floating point formats.[9]

Quantization

The bit depth limits the signal-to-noise ratio (SNR) of the reconstructed signal to a maximum level determined by quantization error. The bit depth has no impact on the frequency response, which is constrained by the sample rate.

Quantization noise is a model of quantization error introduced by the sampling process during analog-to-digital conversion (ADC). It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is nonlinear and signal-dependent.

An 8-bit binary number of the base ten value 149 with the LSB highlighted.

In an ideal ADC, where the quantization error is uniformly distributed between least significant bit (LSB) and where the signal has a uniform distribution covering all quantization levels, the signal-to-quantization-noise ratio (SQNR) can be calculated from

where Q is the number of quantization bits and the result is measured in decibels (dB).[10][11]

24-bit digital audio has a theoretical maximum SNR of 144 dB, compared to 96 dB for 16-bit; however, Template:Asof digital audio converter technology is limited to a SNR of about 124 dB (21-bit)[12] because of real-world limitations in integrated circuit design. Still, this approximately matches the performance of the human auditory system.[13][14]

Signal-to-noise ratio and resolution of bit depths
# bits SNR Possible integer values Base ten signed range
4 24.08 dB 16 −8 to +7
8 48.16 dB 256 −128 to +127
11[15] 66.22 dB 2048 −1024 to +1023
16 96.33 dB 65,536 −32,768 to +32,767
20 120.41 dB 1,048,576 −524,288 to +524,287
24 144.49 dB 16,777,216 −8,388,608 to +8,388,607
32 192.66 dB 4,294,967,296 −2,147,483,648 to +2,147,483,647
48 288.99 dB 281,474,976,710,656 −140,737,488,355,328 to +140,737,488,355,327
64 385.32 dB 18,446,744,073,709,551,616 −9,223,372,036,854,775,808 to +9,223,372,036,854,775,807

The resolution of floating point samples is less straightforward than integer samples, but the benefit comes in the increased accuracy of low values. In floating point representation, the space between any two adjacent values is of the same proportion as the space between any other two adjacent values, whereas in an integer representation, the space between adjacent values gets larger in proportion to low-level signals. This greatly increases the SNR because the accuracy of a high-level signal will be the same as the accuracy of an identical signal at a lower level.[16]

The trade-off between floating point and integers is that the space between large floating point values is greater than the space between large integer values of the same bit depth. Rounding a large floating point number results in a greater error than rounding a small floating point number whereas rounding an integer number will always result in the same level of error. In other words, integers have round-off that is uniform, always rounding the LSB to 0 or 1, and floating point has SNR that is uniform, the quantization noise level is always of a certain proportion to the signal level.[16] A floating point noise floor will rise as the signal rises and fall as the signal falls, resulting in audible variance if the bit depth is low enough.[17]

Audio processing

Most processing operations on digital audio involve requantization of samples, and thus introduce additional rounding error analogous to the original quantization error introduced during analog to digital conversion. To prevent rounding error larger than the implicit error during ADC, calculations during processing must be performed at higher precisions than the input samples.[18]

Digital signal processing (DSP) operations can be performed in either fixed point or floating point precision. In either case, the precision of each operation is determined by the precision of the hardware operations used to perform each step of the processing and not the resolution of the input data. For example, on x86 processors, floating point operations are performed at 32- or 64-bit precision and fixed point operations at 16-, 32- or 64-bit resolution. Consequently, all processing performed on Intel-based hardware will be performed at 16-, 32- or 64-bit integer precision, or 32- or 64-bit floating point precision regardless of the source format. However, if memory is at a premium, software may still choose to output lower resolution 16- or 24-bit audio after higher precision processing.

Fixed point digital signal processors often support unusual word sizes and precisions in order to support specific signal resolutions. For example, the Motorola 56000 DSP chip uses 24-bit word sizes, 24-bit multipliers and 56-bit accumulators to perform multiply-accumulate operations on two 24-bit samples without overflow or rounding.[19] On devices that do not support large accumulators, fixed point operations may be implicitly rounded, reducing precision to below that of the input samples.

Errors compound through multiple stages of DSP at a rate that depends on the operations being performed. For uncorrelated processing steps on audio data without a DC offset, errors are assumed to be random with zero mean. Under this assumption, the standard deviation of the distribution represents the error signal, and quantization error scales with the square root of the number of operations.[20] High levels of precision are necessary for algorithms that involve repeated processing, such as convolution.[18] High levels of precision are also necessary in recursive algorithms, such as infinite impulse response (IIR) filters.[21] In the particular case of IIR filters, rounding error can degrade frequency response and cause instability.[18]

Dither

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The noise introduced by quantization error, including rounding errors and loss of precision introduced during audio processing, can be mitigated by adding a small amount of random noise, called dither, to the signal before quantizing. Dithering eliminates the granularity of quantization error, giving very low distortion, but at the expense of a slightly raised noise floor. Measured using ITU-R 468 noise weighting, this is about 66 dB below alignment level, or 84 dB below digital full scale, which is somewhat lower than the microphone noise level on most recordings, and hence of no consequence in 16-bit audio (see Programme level for more on this).

24-bit audio does not require dithering, as the noise level of the digital converter is always louder than the required level of any dither that might be applied. 24-bit audio could theoretically encode 144 dB of dynamic range, but no ADCs exist that can provide higher than ~125 dB.[22]

Dither can also be used to increase the effective dynamic range. The perceived dynamic range of 16-bit audio can be as high as 120 dB with noise-shaped dither, taking advantage of the frequency response of the human ear.[23]

Dynamic range

Dynamic range is the difference between the largest and smallest signal a system can record or reproduce. Without dither, the dynamic range correlates to the quantization noise floor. For example, 16-bit integer resolution allows for a dynamic range of about 96 dB.

Using higher bit depths during studio recording accommodates greater dynamic range. If the signal's dynamic range is lower than that allowed by the bit depth, the recording has headroom, and the higher the bit depth, the more headroom that's available. This reduces the risk of clipping without encountering quantization errors at low volumes.

With the proper application of dither, digital systems can reproduce signals with levels lower than their resolution would normally allow, extending the effective dynamic range beyond the limit imposed by the resolution.[24]

The use of techniques such as oversampling and noise shaping can further extend the dynamic range of sampled audio by moving quantization error out of the frequency band of interest.

Oversampling

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Oversampling is an alternative method to increase the dynamic range of PCM audio without changing the number of bits per sample.[25] In oversampling, audio samples are acquired at a multiple of the desired sample rate. Because quantization error is assumed to be uniformly distributed with frequency, much of the quantization error is shifted to ultrasonic frequencies, and can be removed by the digital to analog converter during playback.

For an increase equivalent to n additional bits of resolution, a signal must be oversampled by

For example, a 14-bit ADC can produce 16-bit 48 kHz audio if operated at 16x oversampling, or 768 kHz. Oversampled PCM therefore exchanges fewer bits per sample for more samples in order to obtain the same resolution.

Noise shaping

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Oversampling a signal results in equal quantization noise per unit of bandwidth at all frequencies and a dynamic range that improves with only the square root of the oversampling ratio. Noise shaping is a technique that adds additional noise at higher frequencies which cancels out some error at lower frequencies, resulting in a larger increase in dynamic range when oversampling. For nth-order noise shaping, the dynamic range of an oversampled signal is improved by an additional 6n dB relative to oversampling without noise shaping.[26] For example, for a 20 kHz analog audio sampled at 4x oversampling with second order noise shaping, the dynamic range is increased by 30 dB. Therefore a 16-bit signal sampled at 176 kHz would have equal resolution as a 21-bit signal sampled at 44.1 kHz without noise shaping.

Noise shaping is commonly implemented with delta-sigma modulation. Using delta-sigma modulation, Super Audio CD obtains 120 dB SNR at audio frequencies using 1-bit audio with 64x oversampling.

Applications

Bit depth is a fundamental property of digital audio implementations and there are a variety of situations where it is a measurement.

Example applications and bits per sample
Application Description Audio format(s)
CD-DA (Red Book)[27] Digital media 16-bit LPCM
DVD-Audio[28] Digital media 16-, 20- and 24-bit LPCM[note 1]
Super Audio CD[29] Digital media 1-bit Direct Stream Digital (PDM)
Blu-ray Disc audio[30] Digital media 16-, 20- and 24-bit LPCM and others[note 2]
DV audio[31] Digital media 12-bit compressed PCM and 16-bit uncompressed PCM
ITU-T Recommendation G.711[32] Compression standard for telephony 8-bit PCM with companding[note 3]
NICAM-1, NICAM-2 and NICAM-3[33] Compression standards for broadcasting 10-, 11- and 10-bit PCM respectively, with companding[note 4]
Pro Tools 11[34] DAW by Avid Technology 16- and 24-bit or 32-bit floating point sessions and 64-bit floating point mixing
Logic Pro X[35] DAW by Apple Inc. 16- and 24-bit projects
GarageBand '11 (version 6)[36] DAW by Apple Inc. 16-bit default with 24-bit real instrument recording
Live 9[8] DAW by Ableton 32-bit floating point mixing
Reason 7[37] DAW by Propellerhead Software 16-, 20- and 24-bit I/O, 32-bit floating point arithmetic and 64-bit summing

Bit rate and file size

Bit depth affects bit rate and file size. Bit rate refers to the amount of data, specifically bits, transmitted or received per second.

See also

Notes

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References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  1. ↑ Thompson, Dan (2005). Understanding Audio. Berklee Press. ISBN 978-0-634-00959-4.
  2. ↑ Template:Cite web
  3. ↑ Template:Cite web
  4. ↑ Template:Cite web
  5. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  6. ↑ Template:Cite web
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  8. ↑ 8.0 8.1 Template:Cite web
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  10. ↑ See Signal-to-noise ratio#Fixed point)
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  12. ↑ Template:Cite web
  13. ↑ Template:Cite web
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  15. ↑ This is the bit depth that the Raspberry Pi uses when driving the pulse-width modulator of its BCM2835 chip
  16. ↑ 16.0 16.1 Template:Cite web
  17. ↑ Template:Cite web
  18. ↑ 18.0 18.1 18.2 Template:Cite web
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  20. ↑ Template:Cite web
  21. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  22. ↑ Choosing a high-performance audio ADC - "I went looking for the best dynamic range audio ADC I could find" and highest are 123 dB dynamic range
  23. ↑ Template:Cite web
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