275:
762:
whereas rounding an integer number will always result in the same level of error. In other words, integers have a round-off that is uniform, always rounding the LSB to 0 or 1, and the floating-point format has uniform SNR, the quantization noise level is always of a certain proportion to the signal level. A floating-point noise floor rises as the signal rises and falls as the signal falls, resulting in audible variance if the bit depth is low enough.
40:
827:
810:
on audio data without a DC offset, errors are assumed to be random with zero means. 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. High levels of precision are necessary for algorithms that involve repeated processing, such as
1088: dB relative to oversampling without noise shaping. For example, for a 20 kHz analog audio sampled at 4Γ 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 a bit depth equal to a 21-bit signal sampled at 44.1 kHz without noise shaping.
1079:
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
914:
Oversampling is an alternative method to increase the dynamic range of PCM audio without changing the number of bits per sample. 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
809:
on two 24-bit samples without overflow or truncation. On devices that do not support large accumulators, fixed-point results may be truncated, reducing precision. Errors compound through multiple stages of DSP at a rate that depends on the operations being performed. For uncorrelated processing steps
2361:
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
1051:
Dynamic range can also be enhanced with oversampling at signal reconstruction, absent oversampling at the source. Consider 16Γ oversampling at reconstruction. Each sample at reconstruction would be unique in that for each of the original sample points sixteen are inserted, all having been calculated
761:
The trade-off between floating-point and integer formats 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
857:
24-bit and 32-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, and 32-bit audio can achieve 192 dB, but this is
880:
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. With the proper application of dither,
1059:
Historical noteβThe compact disc standard was developed by a collaboration between Sony and
Philips. The first Sony consumer unit featured a 16-bit DAC; the first Philips units had dual 14-bit DACs. This confused the marketplace and even in professional circles, because 14-bit PCM allows for
770:
Most processing operations on digital audio involve the re-quantization of samples and thus introduce additional rounding errors analogous to the original quantization error introduced during analog-to-digital conversion. To prevent rounding errors larger than the implicit error during ADC,
215:
file format support floating-point representations. 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
757:
The resolution of floating-point samples is less straightforward than integer samples because floating-point values are not evenly spaced. In floating-point representation, the space between any two adjacent values is in proportion to the value.
432:
464:. Multiple converters can be used to cover different ranges of the same signal, being combined to record a wider dynamic range in the long-term, while still being limited by the single converter's dynamic range in the short term, which is called
781:
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
2362:
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.
2062:
1047:
For example, a 14-bit ADC can produce 16-bit 48 kHz audio if operated at 16Γ oversampling, or 768 kHz. Oversampled PCM, therefore, exchanges fewer bits per sample for more samples to obtain the same resolution.
1064:
which theoretically realized the full 96 dB dynamic range of the CD format. In practice the
Philips CD100 was rated at 90 dB SNR in the audio band of 20 Hzβ20 kHz, the same as Sony's CDP-101.
881:
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. The use of techniques such as
1042:
172:
as the word length increases: adding one bit doubles the resolution, adding two quadruples it, and so on. The number of possible values that an integer bit depth can represent can be calculated by using
1056:. The mechanism of increased effective bit depth is as previously discussed, that is, quantization noise power has not been reduced, but the noise spectrum has been spread over 16Γ the audio bandwidth.
794:, and fixed-point operations at 16-, 32- or 64-bit resolution. Consequently, all processing performed on Intel-based hardware will be performed with these constraints regardless of the source format.
145:
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
452:
has a theoretical maximum SNR of 98 dB, and professional 24-bit digital audio tops out as 146 dB. As of 2011, digital audio converter technology is limited to an SNR of about 123 dB (
1107:
Bit depth is a fundamental property of digital audio implementations. Depending on application requirements and equipment capabilities, different bit depths are used for different applications.
834:
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
1567:
Intel and AMD x86 hardware can handle higher precision than 64 bits, or even arbitrarily large floating-point numbers or integers, but processing takes a lot longer than the native types.
322:
2398:
One of the great discoveries in PCM was that by adding a small random noise (that we call dither) the truncation effect can disappear. Even more important was the realization that there is a
1486:
and file size. Bits are the basic unit of data used in computing and digital communications. Bit rate refers to the amount of data, specifically bits, transmitted or received per second. In
1558:
While 32-bit converters exist, they are purely for marketing purposes and provide no practical benefit over 24-bit converters; the extra bits are either zero or encode only noise.
337:
2638:
2418:
838:, to the signal before quantizing. Dithering eliminates non-linear quantization error behavior, giving very low distortion, but at the expense of a slightly raised
168:
The resolution indicates the number of discrete values that can be represented over the range of analog values. The resolution of binary integers increases
1993:
43:
An analog signal (in red) encoded to 4-bit PCM digital samples (in blue); the bit depth is four, so each sample's amplitude is one of 16 possible values.
2859:
1952:
So your 32-bit DAC is only ever going to be able to output at most 21 bits of useful data, and the other bits will be masked by circuit noise.
1895:
Dynamic Range (β60 dB input, A-weighted): 124 dB typical
Dynamic Range (β60 dB input, 20 kHz bandwidth): 122 dB typical
2451:
2375:
2119:"The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 28 β Digital Signal Processors / Fixed versus Floating Point"
885:
and noise shaping can further extend the dynamic range of sampled audio by moving quantization error out of the frequency band of interest.
2032:
2583:
932:
492:
267:
as quantization noise. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is
2726:
2671:
2144:
787:
2999:
2093:
1596:
2340:
2645:
2076:
Christodoulou, Lakis; Lane, John; Kasparis, Takis (1 March 2010). "Dynamic range extension using multiple A/D converters".
1788:"The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 4 β DSP Software / Floating Point (Real Numbers)"
818:(IIR) filters. In the particular case of IIR filters, rounding error can degrade frequency response and cause instability.
2425:
2939:
2758:
1646:
889:
328:
293:
118:
17:
2186:
483:
2834:
1444:
Blu-ray supports a variety of non-LPCM formats but all conform to some combination of 16, 20, or 24 bits per sample.
858:
almost impossible to achieve in the real world, as even the best sensors and microphones rarely exceed 130 dB.
2727:"DIGITAL SOUND SIGNALS: tests to compare the performance of five companding systems for high-quality sound signals"
2242:"The Scientist and Engineer's Guide to Digital Signal Processing, Chapter 4 β DSP Software / Number Precision"
2784:
2402:
sort of random noise to add and that when the right dither is used, the resolution of the digital system becomes
1871:
24-bit DACs often only manage approximately 16-bit performance and the very best reach 21-bit (ENOB) performance
2289:
2000:
854:, which is comparable to the microphone and room noise level, and hence of little consequence in 16-bit audio.
133:
A PCM signal is a sequence of digital audio samples containing the data providing the necessary information to
2187:"Relationship of Data Word Size to Dynamic Range and Signal Quality in Digital Audio Processing Applications"
1491:
1367:
1361:
1295:
1275:
806:
212:
2866:
2639:"White paper Blu-ray Disc Format, 2.B Audio Visual Application Format Specifications for BD-ROM Version 2.4"
2557:
1935:
260:
64:
1060:
84 dB SNR, 12 dB less than 16-bit PCM. Philips had implemented 4Γ oversampling with first order
228:, and an exponent determining a power-of-two factor to scale the mantissa. The mantissa is expressed as a
1826:
1812:
1494:, bit rate describes the amount of information used to encode an audio signal. It is usually measured in
916:
2313:
1615:
Mathematics of the
Discrete Fourier Transform (DFT) with Audio Applications, Second Edition, online book
1360:
8-bit PCM, 16-bit PCM, 24-bit PCM, 32-bit PCM, 32-bit FP, 64-bit FP, 4-bit IMA ADPCM & 2-bit cADPCM
427:{\displaystyle {\text{SQNR}}=20\log _{10}({\sqrt {1.5}}\cdot 2^{b})\approx (1.76+6.02\,b)\ {\text{dB}},}
2483:
2045:
The practical dynamic range could be said to be from the threshold of hearing to the threshold of pain
72:
1764:
1741:
1610:
1693:
1507:
1428:
1250:
1099:
achieves a theoretical 120 dB SNR at audio frequencies using 1-bit audio with 64Γ oversampling.
843:
815:
774:
204:
2262:
Carletta, Joan (2003). "Determining appropriate precisions for signals in fixed-point IIR filters".
2458:
2272:
2028:
1518:
1170:
798:
453:
2382:
2215:
1980:
all the '32-bit capable' DAC chips existent today have an actual resolution less than 24 bit.
2809:
1827:"Taking the Mystery out of the Infamous Formula, "SNR = 6.02N + 1.76dB," and Why You Should Care"
1389:
1254:
1084:
th-order noise shaping, the dynamic range of an oversampled signal is improved by an additional 6
2508:
830:
Headroom and noise floor at audio process stages for the purpose of comparison with dither level
3019:
2964:
2616:
2522:
2267:
1923:
128dB SNR ('A'-weighted mono @ 48 kHz) 123 dB SNR (non-weighted stereo @ 48 kHz)
1855:
1338:
1092:
896:
can make headroom available while maintaining the same dynamic range. This reduces the risk of
778:
1636:
801:
often supports specific word lengths to support specific signal resolutions. For example, the
771:
calculations during processing must be performed at higher precisions than the input samples.
2590:
1166:
1096:
1053:
888:
If the signal's maximum level is lower than that allowed by the bit depth, the recording has
324:
241:
134:
91:
52:
327:(LSB) and where the signal has a uniform distribution covering all quantization levels, the
2145:"48-Bit Integer Processing Beats 32-Bit Floating-Point for Professional Audio Applications"
1883:
1670:
1432:
2078:
2010 4th
International Symposium on Communications, Control and Signal Processing (ISCCSP)
1907:
8:
2733:
915:
of the quantization error is shifted to ultrasonic frequencies and can be removed by the
193:
207:(DAWs) support PCM formats with samples represented by floating-point numbers. Both the
86:
In basic implementations, variations in bit depth primarily affect the noise level from
2679:
2295:
2099:
457:
249:
245:
87:
2536:
2348:
1964:
1718:
2995:
2285:
2089:
1642:
1592:
1245:
1191:
122:
2299:
2155:
2103:
2060:, "Multiple A to D converters for enhanced dynamic range", issued 1999-07-01
1080:
frequencies, resulting in a larger increase in dynamic range when oversampling. For
2336:
2277:
2081:
2057:
1542:
897:
893:
791:
264:
110:
can mitigate these effects without changing the bit depth. Bit depth also affects
2913:
2701:
1269:
1178:
847:
461:
229:
2085:
2194:
1833:
1157:
814:. High levels of precision are also necessary in recursive algorithms, such as
802:
290:
In an ideal ADC, where the quantization error is uniformly distributed between
169:
150:
1366:
8-bit int, 16-bit int, 24-bit int, 32-bit int, 32-bit float, and 64-bit float
3013:
1343:
16-, 20- and 24-bit I/O, 32-bit floating point arithmetic and 64-bit summing
1074:
1061:
877:
866:
154:
138:
103:
95:
48:
2762:
1470:
NICAM systems 1, 2 and 3 compress down from 13, 14 and 14 bits respectively.
1318:
1274:
16- and 24-bit or 32-bit floating point sessions and 64-bit floating point
1235:
909:
882:
174:
107:
80:
2281:
1546:
1512:
1461:
companding algorithms, compressing down from 13 and 14 bits respectively.
839:
811:
253:
225:
200:
162:
274:
1408:
1375:
1289:
1221:
851:
460:
design. Still, this approximately matches the performance of the human
189:
2891:
2118:
1402:
1308:
1282:
1215:
1144:
869:
dither, taking advantage of the frequency response of the human ear.
861:
Dither can also be used to increase the effective dynamic range. The
268:
142:
76:
2241:
1787:
805:
DSP chip uses 24-bit multipliers and 56-bit accumulators to perform
27:
Number of bits of information recorded for each digital audio sample
1483:
1313:
Allows audio processing precision to 32-bit float or 64-bit float
244:(SNR) of the reconstructed signal to a maximum level determined by
221:
217:
111:
39:
31:
1458:
1037:{\displaystyle \mathrm {number\ of\ samples} =(2^{n})^{2}=2^{2n}.}
441:
is the number of quantization bits, and the result is measured in
2558:"Sweetwater Knowledge Base, Masterlink: What is a "Red Book" CD?"
1324:
442:
283:
146:
1765:"Audio File Format Specifications, AIFF / AIFF-C Specifications"
1413:
16- and 24-bit int and 32-bit floating point (controlled by OS)
472:
Signal-to-noise ratio and resolution of bit depths (unweighted)
2702:"G.711 : Pulse code modulation (PCM) of voice frequencies"
1354:
1348:
1302:
926:
additional bits of resolution, a signal must be oversampled by
835:
182:
99:
865:
dynamic range of 16-bit audio can be 120 dB or more with
1454:
1228:
1209:
1205:
1127:
842:. Recommended dither for 16-bit digital audio measured using
279:
157:
with a fixed number of digits – the sample's
1294:
16- and 24-bit projects and 32-bit or 64-bit floating point
2965:"Sample Rate, Bit-Depth & Bitrate | Exclusivemusicplus"
2264:
Proceedings of the 40th annual Design
Automation Conference
1719:"Ableton Reference Manual Version 10, 32. Audio Fact Sheet"
1495:
1137:
826:
224:
representing whether the number is positive or negative, a
1936:"The great audio myth: why you don't need that 32-bit DAC"
1638:
Pro Tools 10 Advanced Music
Production Techniques, pg. 247
2075:
1538:
1487:
786:
processors, floating-point operations are performed with
783:
208:
60:
1742:"Audio File Format Specifications, WAVE Specifications"
900:
without increasing quantization errors at low volumes.
449:
185:
system has a resolution of 65,536 (2) possible values.
2732:. BBC Research Department. August 1978. Archived from
2644:. Blu-ray Disc Association. April 2010. Archived from
2341:"24/192 Music Downloads ...and why they make no sense"
1240:
10-, 11- and 10-bit PCM respectively, with companding
297:
1384:
16-bit default with 24-bit real instrument recording
935:
340:
296:
2785:"Pro Tools Documentation, Pro Tools Reference Guide"
1329:32-bit floating point bit depth and 64-bit summing
1111:Example applications and supported audio bit depth
456:21 bits) because of real-world limitations in
83:, which can support up to 24 bits per sample.
2116:
2016:The dynamic range of human hearing is 120 dB
1581:
1036:
426:
316:
317:{\displaystyle \scriptstyle {\pm {\frac {1}{2}}}}
3011:
2537:"B.1 First and Second-Order Noise Shaping Loops"
1785:
1634:
2989:
2669:
2180:
2178:
2176:
2865:. Propellerhead Software. 2013. Archived from
2751:
1713:
1711:
1662:
1515:, the corresponding concept for digital images
1397:16- and 24-bit LPCM and 32-bit floating point
188:Integer PCM audio data is typically stored as
71:of each sample. Examples of bit depth include
2142:
2136:
1608:
872:
2852:
2827:
2173:
1762:
1739:
1691:
1668:
1628:
777:(DSP) operations can be performed in either
2802:
2614:
2419:"Dithering in Analog-to-Digital Conversion"
2184:
1908:"WM8741 : High-Performance Stereo DAC"
1708:
1091:Noise shaping is commonly implemented with
2994:(4th ed.). McGraw-Hill Professional.
2892:"GarageBand '11: Set the audio resolution"
2884:
2424:. e2v Semiconductors. 2007. Archived from
2335:
2239:
2110:
1991:
1685:
75:, which uses 16 bits per sample, and
2271:
1779:
1602:
1545:representation of the signal, not on the
1477:
448:Therefore, 16-bit digital audio found on
406:
232:in IEEE base-two floating-point formats.
2906:
2761:. Ardour Community. 2014. Archived from
2608:
2576:
2261:
1813:Signal-to-noise ratio Β§ Fixed point
825:
273:
128:
38:
2707:. International Telecommunication Union
2663:
1853:
220:, which is composed of three fields: a
121:. Non-PCM formats, such as those using
117:Bit depth is useful for describing PCM
14:
3012:
2777:
2631:
2373:
1824:
1756:
1733:
2719:
2315:Choosing a high-performance audio ADC
259:Quantization error introduced during
248:. The bit depth has no impact on the
125:, do not have associated bit depths.
67:, and it directly corresponds to the
30:For other uses of "8-bit music", see
2990:Ken C. Pohlmann (15 February 2000).
2694:
2550:
2381:. Meridian Audio Ltd. Archived from
1856:"NwAvGuy: Noise & Dynamic Range"
1186:16-, 20- and 24-bit LPCM and others
2376:"Coding High Quality Digital Audio"
1541:, quantization is performed on the
765:
24:
2449:
985:
982:
979:
976:
973:
970:
967:
961:
958:
952:
949:
946:
943:
940:
937:
892:. Using higher bit depths during
329:signal-to-quantization-noise ratio
25:
3031:
2589:. Sonic Solutions. Archived from
2452:"Oversampling Interpolating DACs"
1427:DVD-Audio also supports optional
752:
2457:. Analog Devices. Archived from
2143:Moorer, James (September 1999).
2035:from the original on 4 June 2011
1200:12- and 16-bit uncompressed PCM
1095:. Using delta-sigma modulation,
1068:
2957:
2932:
2529:
2515:
2501:
2476:
2443:
2411:
2367:
2329:
2306:
2255:
2233:
2208:
2069:
2050:
2021:
1985:
1957:
1928:
1900:
1876:
1847:
1818:
1805:
1763:Kabal, Peter (3 January 2011).
1740:Kabal, Peter (3 January 2011).
1561:
1552:
1464:
1447:
1438:
1421:
1102:
903:
235:
2670:Puhovski, Nenad (April 2000).
1549:samples relevant to bit depth.
1531:
1492:lossy compressed audio formats
1006:
992:
922:For an increase equivalent to
850:, or 84 dB below digital
807:multiply-accumulate operations
410:
394:
388:
365:
331:(SQNR) can be calculated from
252:, which is constrained by the
98:. However, techniques such as
13:
1:
1692:Price, Simon (October 2005).
1611:"Pulse Code Modulation (PCM)"
1574:
744:β9,223,372,036,854,775,808 to
141:. Each sample represents the
1854:Nwavguy (6 September 2011).
261:analog-to-digital conversion
7:
2992:Principles of Digital Audio
2920:. Audacity development team
2860:"Reason 7 Operation Manual"
2615:Shapiro, L. (2 July 2001).
2564:. Sweetwater. 27 April 2007
2240:Smith, Steven (1997β1998).
2117:Smith, Steven (1997β1998).
2086:10.1109/ISCCSP.2010.5463427
1694:"Reason Mixing Masterclass"
1669:Wherry, Mark (March 2012).
1501:
917:digital-to-analog converter
746:+9,223,372,036,854,775,807
286:), with the LSB highlighted
10:
3036:
2374:Stuart, J. Robert (1997).
2029:"Sensitivity of Human Ear"
1994:"Aspects of Human Hearing"
1234:Compression standards for
1072:
907:
873:Dynamic range and headroom
846:is about 66 dB below
741:18,446,744,073,709,551,616
514:for signed representation
205:digital audio workstations
181:is the bit depth. Thus, a
73:Compact Disc Digital Audio
29:
2810:"Logic Pro X: User Guide"
2617:"Surround Sound, Page 10"
2584:"Understanding DVD-Audio"
1786:Smith, Steven (1997β98).
1635:Campbell, Robert (2013).
1508:Audio system measurements
1429:Meridian Lossless Packing
1394:Open source audio editor
1257:and the Ardour Community
1214:Compression standard for
1152:16-, 20- and 24-bit LPCM
844:ITU-R 468 noise weighting
821:
816:infinite impulse response
799:digital signal processors
775:Digital signal processing
671:β8,388,608 to +8,388,607
240:The bit depth limits the
2835:"Cubase Pro 10.5 Manual"
1524:
1519:Effective number of bits
1231:-1, NICAM-2 and NICAM-3
2484:"The history of the CD"
719:β140,737,488,355,328 to
466:dynamic range extension
63:of information in each
2894:. Apple. 13 March 2012
2672:"DV β A SUCCESS STORY"
1609:Smith, Julius (2007).
1587:Thompson, Dan (2005).
1478:Bit rate and file size
1339:Propellerhead Software
1260:32-bit floating point
1093:delta-sigma modulation
1038:
831:
507:No. of possible values
428:
318:
287:
282:binary number (149 in
271:and signal-dependent.
161:, also referred to as
44:
2918:wiki.audacityteam.com
2815:. Apple. January 2010
2759:"Ardour Key Features"
2282:10.1145/775832.775998
1965:"32-bit capable DACs"
1825:Kester, Walt (2007).
1167:Direct Stream Digital
1097:Direct Stream Digital
1054:reconstruction filter
1039:
829:
721:+140,737,488,355,327
652:β524,288 to +524,287
633:β131,072 to +131,071
429:
325:least significant bit
319:
277:
242:signal-to-noise ratio
153:number, encoded as a
129:Binary representation
92:signal-to-noise ratio
53:pulse-code modulation
42:
2914:"Audacity: Features"
2266:. pp. 656β661.
1641:. Cengage Learning.
1453:ITU-T specifies the
1433:lossless compression
933:
338:
294:
211:file format and the
2318:, 14 September 2011
2161:on 14 February 2019
2152:www.jamminpower.com
1767:. McGill University
1744:. McGill University
1671:"Avid Pro Tools 10"
1589:Understanding Audio
1112:
716:281,474,976,710,656
665:0.000008717 dB
614:β32,768 to +32,767
473:
2969:Exclusivemusicplus
2944:www.image-line.com
2739:on 8 November 2012
2682:on 27 October 2004
2562:www.sweetwater.com
1482:Bit depth affects
1381:DAW by Apple Inc.
1179:Blu-ray Disc audio
1110:
1034:
832:
512:Range (per sample)
471:
458:integrated circuit
424:
314:
313:
288:
250:frequency response
246:quantization error
199:Today, most audio
88:quantization error
45:
18:Resolution (audio)
3001:978-0-07-134819-5
2971:. 26 October 2018
2840:. Steinberg. 2020
2431:on 4 October 2011
2339:(25 March 2012).
2337:Montgomery, Chris
2185:Tomarakos, John.
2095:978-1-4244-6285-8
2006:on 21 August 2011
1942:. 19 January 2016
1940:Android Authority
1597:978-0-634-00959-4
1591:. Berklee Press.
1417:
1416:
966:
957:
919:during playback.
750:
749:
694:β2,147,483,648 to
646:0.0001165 dB
627:0.0004201 dB
594:β2,048 to +2,047
574:β1,024 to +1,023
419:
415:
373:
344:
310:
123:lossy compression
59:is the number of
16:(Redirected from
3027:
3005:
2981:
2980:
2978:
2976:
2961:
2955:
2954:
2952:
2950:
2940:"Audio Settings"
2936:
2930:
2929:
2927:
2925:
2910:
2904:
2903:
2901:
2899:
2888:
2882:
2881:
2879:
2877:
2871:
2864:
2856:
2850:
2849:
2847:
2845:
2839:
2831:
2825:
2824:
2822:
2820:
2814:
2806:
2800:
2799:
2797:
2795:
2789:
2781:
2775:
2774:
2772:
2770:
2755:
2749:
2748:
2746:
2744:
2738:
2731:
2723:
2717:
2716:
2714:
2712:
2706:
2698:
2692:
2691:
2689:
2687:
2678:. Archived from
2676:www.stanford.edu
2667:
2661:
2660:
2658:
2656:
2650:
2643:
2635:
2629:
2628:
2626:
2624:
2612:
2606:
2605:
2603:
2601:
2595:
2588:
2580:
2574:
2573:
2571:
2569:
2554:
2548:
2547:
2545:
2543:
2533:
2527:
2526:
2519:
2513:
2512:
2505:
2499:
2498:
2496:
2494:
2480:
2474:
2473:
2471:
2469:
2463:
2456:
2447:
2441:
2440:
2438:
2436:
2430:
2423:
2415:
2409:
2408:
2395:
2393:
2387:
2380:
2371:
2365:
2364:
2358:
2356:
2347:. Archived from
2333:
2327:
2326:
2325:
2323:
2310:
2304:
2303:
2275:
2259:
2253:
2252:
2250:
2248:
2237:
2231:
2230:
2228:
2226:
2220:
2212:
2206:
2205:
2203:
2201:
2182:
2171:
2170:
2168:
2166:
2160:
2154:. Archived from
2149:
2140:
2134:
2133:
2131:
2129:
2123:www.dspguide.com
2114:
2108:
2107:
2080:. pp. 1β4.
2073:
2067:
2066:
2065:
2061:
2054:
2048:
2047:
2042:
2040:
2025:
2019:
2018:
2013:
2011:
2005:
1999:. Archived from
1998:
1992:D. R. Campbell.
1989:
1983:
1982:
1977:
1975:
1961:
1955:
1954:
1949:
1947:
1932:
1926:
1925:
1920:
1918:
1904:
1898:
1897:
1892:
1890:
1880:
1874:
1873:
1868:
1866:
1851:
1845:
1844:
1842:
1840:
1831:
1822:
1816:
1809:
1803:
1802:
1800:
1798:
1792:www.dspguide.com
1783:
1777:
1776:
1774:
1772:
1760:
1754:
1753:
1751:
1749:
1737:
1731:
1730:
1728:
1726:
1715:
1706:
1705:
1703:
1701:
1696:. Sound On Sound
1689:
1683:
1682:
1680:
1678:
1673:. Sound On Sound
1666:
1660:
1659:
1657:
1655:
1632:
1626:
1625:
1623:
1621:
1606:
1600:
1585:
1568:
1565:
1559:
1556:
1550:
1543:frequency-domain
1537:For example, in
1535:
1471:
1468:
1462:
1451:
1445:
1442:
1436:
1425:
1378:'11 (version 6)
1122:Audio format(s)
1113:
1109:
1043:
1041:
1040:
1035:
1030:
1029:
1014:
1013:
1004:
1003:
988:
964:
955:
894:studio recording
792:double precision
766:Audio processing
737:
712:
687:
608:0.001497 dB
504:rounding error)
494:
485:
474:
470:
433:
431:
430:
425:
420:
417:
413:
387:
386:
374:
369:
361:
360:
345:
342:
323:
321:
320:
315:
312:
311:
303:
194:two's complement
21:
3035:
3034:
3030:
3029:
3028:
3026:
3025:
3024:
3010:
3009:
3008:
3002:
2985:
2984:
2974:
2972:
2963:
2962:
2958:
2948:
2946:
2938:
2937:
2933:
2923:
2921:
2912:
2911:
2907:
2897:
2895:
2890:
2889:
2885:
2875:
2873:
2869:
2862:
2858:
2857:
2853:
2843:
2841:
2837:
2833:
2832:
2828:
2818:
2816:
2812:
2808:
2807:
2803:
2793:
2791:
2787:
2783:
2782:
2778:
2768:
2766:
2765:on 8 April 2014
2757:
2756:
2752:
2742:
2740:
2736:
2729:
2725:
2724:
2720:
2710:
2708:
2704:
2700:
2699:
2695:
2685:
2683:
2668:
2664:
2654:
2652:
2648:
2641:
2637:
2636:
2632:
2622:
2620:
2613:
2609:
2599:
2597:
2596:on 4 March 2012
2593:
2586:
2582:
2581:
2577:
2567:
2565:
2556:
2555:
2551:
2541:
2539:
2535:
2534:
2530:
2521:
2520:
2516:
2509:"Philips CD100"
2507:
2506:
2502:
2492:
2490:
2482:
2481:
2477:
2467:
2465:
2461:
2454:
2448:
2444:
2434:
2432:
2428:
2421:
2417:
2416:
2412:
2391:
2389:
2388:on 7 April 2016
2385:
2378:
2372:
2368:
2354:
2352:
2334:
2330:
2321:
2319:
2312:
2311:
2307:
2292:
2260:
2256:
2246:
2244:
2238:
2234:
2224:
2222:
2218:
2214:
2213:
2209:
2199:
2197:
2183:
2174:
2164:
2162:
2158:
2147:
2141:
2137:
2127:
2125:
2115:
2111:
2096:
2074:
2070:
2063:
2056:
2055:
2051:
2038:
2036:
2027:
2026:
2022:
2009:
2007:
2003:
1996:
1990:
1986:
1973:
1971:
1963:
1962:
1958:
1945:
1943:
1934:
1933:
1929:
1916:
1914:
1906:
1905:
1901:
1888:
1886:
1882:
1881:
1877:
1864:
1862:
1852:
1848:
1838:
1836:
1829:
1823:
1819:
1810:
1806:
1796:
1794:
1784:
1780:
1770:
1768:
1761:
1757:
1747:
1745:
1738:
1734:
1724:
1722:
1721:. Ableton. 2019
1717:
1716:
1709:
1699:
1697:
1690:
1686:
1676:
1674:
1667:
1663:
1653:
1651:
1649:
1633:
1629:
1619:
1617:
1607:
1603:
1586:
1582:
1577:
1572:
1571:
1566:
1562:
1557:
1553:
1536:
1532:
1527:
1504:
1480:
1475:
1474:
1469:
1465:
1452:
1448:
1443:
1439:
1426:
1422:
1270:Avid Technology
1220:8-bit PCM with
1208:Recommendation
1105:
1077:
1071:
1022:
1018:
1009:
1005:
999:
995:
936:
934:
931:
930:
912:
906:
875:
848:alignment level
824:
768:
755:
745:
735:
720:
710:
696:+2,147,483,647
695:
685:
588:0.01807 dB
568:0.03321 dB
513:
508:
503:
501:
499:
498:Minimum dB step
490:
481:
462:auditory system
416:
382:
378:
368:
356:
352:
341:
339:
336:
335:
302:
298:
295:
292:
291:
238:
230:binary fraction
131:
119:digital signals
114:and file size.
35:
28:
23:
22:
15:
12:
11:
5:
3033:
3023:
3022:
3007:
3006:
3000:
2986:
2983:
2982:
2956:
2931:
2905:
2883:
2872:on 24 May 2013
2851:
2826:
2801:
2776:
2750:
2718:
2693:
2662:
2651:on 8 July 2011
2630:
2607:
2575:
2549:
2528:
2523:"Sony CDP-101"
2514:
2500:
2475:
2464:on 19 May 2012
2450:Kester, Walt.
2442:
2410:
2366:
2351:on 7 July 2013
2328:
2305:
2290:
2273:10.1.1.92.1266
2254:
2232:
2207:
2195:Analog Devices
2191:www.analog.com
2172:
2135:
2109:
2094:
2068:
2049:
2020:
1984:
1969:hydrogenaud.io
1956:
1927:
1899:
1875:
1846:
1834:Analog Devices
1817:
1804:
1778:
1755:
1732:
1707:
1684:
1661:
1648:978-1133728016
1647:
1627:
1601:
1579:
1578:
1576:
1573:
1570:
1569:
1560:
1551:
1529:
1528:
1526:
1523:
1522:
1521:
1516:
1510:
1503:
1500:
1479:
1476:
1473:
1472:
1463:
1446:
1437:
1419:
1418:
1415:
1414:
1411:
1405:
1399:
1398:
1395:
1392:
1386:
1385:
1382:
1379:
1372:
1371:
1358:
1351:
1345:
1344:
1341:
1335:
1331:
1330:
1327:
1321:
1315:
1314:
1311:
1305:
1299:
1298:
1292:
1286:
1279:
1278:
1272:
1266:
1262:
1261:
1258:
1248:
1242:
1241:
1238:
1232:
1225:
1224:
1218:
1212:
1202:
1201:
1198:
1197:Digital media
1195:
1188:
1187:
1184:
1183:Digital media
1181:
1175:
1174:
1163:
1160:
1158:Super Audio CD
1154:
1153:
1150:
1147:
1141:
1140:
1134:
1133:Digital media
1131:
1124:
1123:
1120:
1117:
1104:
1101:
1073:Main article:
1070:
1067:
1045:
1044:
1033:
1028:
1025:
1021:
1017:
1012:
1008:
1002:
998:
994:
991:
987:
984:
981:
978:
975:
972:
969:
963:
960:
954:
951:
948:
945:
942:
939:
908:Main article:
905:
902:
874:
871:
823:
820:
803:Motorola 56000
767:
764:
754:
753:Floating point
751:
748:
747:
742:
739:
732:
730:
729:387.08 dB
727:
723:
722:
717:
714:
707:
705:
704:290.75 dB
702:
698:
697:
692:
689:
682:
680:
679:194.42 dB
677:
673:
672:
669:
666:
663:
661:
660:146.26 dB
658:
654:
653:
650:
647:
644:
642:
641:122.17 dB
639:
635:
634:
631:
628:
625:
623:
622:110.13 dB
620:
616:
615:
612:
609:
606:
605:107.12 dB
603:
600:
596:
595:
592:
589:
586:
583:
580:
576:
575:
572:
569:
566:
563:
560:
556:
555:
552:
549:
548:0.1958 dB
546:
543:
540:
536:
535:
532:
529:
526:
523:
520:
516:
515:
510:
505:
496:
487:
478:
435:
434:
423:
412:
409:
405:
402:
399:
396:
393:
390:
385:
381:
377:
372:
367:
364:
359:
355:
351:
348:
309:
306:
301:
237:
234:
165:or word size.
151:floating-point
130:
127:
26:
9:
6:
4:
3:
2:
3032:
3021:
3020:Digital audio
3018:
3017:
3015:
3003:
2997:
2993:
2988:
2987:
2970:
2966:
2960:
2945:
2941:
2935:
2919:
2915:
2909:
2893:
2887:
2868:
2861:
2855:
2836:
2830:
2811:
2805:
2786:
2780:
2764:
2760:
2754:
2735:
2728:
2722:
2703:
2697:
2681:
2677:
2673:
2666:
2647:
2640:
2634:
2619:. ExtremeTech
2618:
2611:
2592:
2585:
2579:
2563:
2559:
2553:
2538:
2532:
2525:. hifiengine.
2524:
2518:
2511:. hifiengine.
2510:
2504:
2489:
2485:
2479:
2460:
2453:
2446:
2427:
2420:
2414:
2407:
2405:
2401:
2384:
2377:
2370:
2363:
2350:
2346:
2342:
2338:
2332:
2317:
2316:
2309:
2301:
2297:
2293:
2287:
2283:
2279:
2274:
2269:
2265:
2258:
2243:
2236:
2217:
2211:
2196:
2192:
2188:
2181:
2179:
2177:
2157:
2153:
2146:
2139:
2124:
2120:
2113:
2105:
2101:
2097:
2091:
2087:
2083:
2079:
2072:
2059:
2053:
2046:
2034:
2030:
2024:
2017:
2002:
1995:
1988:
1981:
1970:
1966:
1960:
1953:
1941:
1937:
1931:
1924:
1913:
1909:
1903:
1896:
1885:
1879:
1872:
1861:
1857:
1850:
1835:
1828:
1821:
1814:
1808:
1793:
1789:
1782:
1766:
1759:
1743:
1736:
1720:
1714:
1712:
1695:
1688:
1672:
1665:
1650:
1644:
1640:
1639:
1631:
1616:
1612:
1605:
1598:
1594:
1590:
1584:
1580:
1564:
1555:
1548:
1544:
1540:
1534:
1530:
1520:
1517:
1514:
1511:
1509:
1506:
1505:
1499:
1497:
1493:
1489:
1485:
1467:
1460:
1456:
1450:
1441:
1434:
1430:
1424:
1420:
1412:
1410:
1406:
1404:
1401:
1400:
1396:
1393:
1391:
1388:
1387:
1383:
1380:
1377:
1374:
1373:
1370:
1369:
1363:
1359:
1356:
1352:
1350:
1347:
1346:
1342:
1340:
1336:
1333:
1332:
1328:
1326:
1322:
1320:
1317:
1316:
1312:
1310:
1306:
1304:
1301:
1300:
1297:
1293:
1291:
1287:
1284:
1281:
1280:
1277:
1273:
1271:
1267:
1265:Pro Tools 11
1264:
1263:
1259:
1256:
1252:
1249:
1247:
1244:
1243:
1239:
1237:
1233:
1230:
1227:
1226:
1223:
1219:
1217:
1213:
1211:
1207:
1204:
1203:
1199:
1196:
1193:
1190:
1189:
1185:
1182:
1180:
1177:
1176:
1172:
1168:
1164:
1162:Digital media
1161:
1159:
1156:
1155:
1151:
1149:Digital media
1148:
1146:
1143:
1142:
1139:
1135:
1132:
1129:
1126:
1125:
1121:
1118:
1115:
1114:
1108:
1100:
1098:
1094:
1089:
1087:
1083:
1076:
1075:Noise shaping
1069:Noise shaping
1066:
1063:
1062:noise shaping
1057:
1055:
1052:by a digital
1049:
1031:
1026:
1023:
1019:
1015:
1010:
1000:
996:
989:
929:
928:
927:
925:
920:
918:
911:
901:
899:
895:
891:
886:
884:
879:
878:Dynamic range
870:
868:
864:
859:
855:
853:
849:
845:
841:
837:
828:
819:
817:
813:
808:
804:
800:
795:
793:
789:
785:
780:
776:
772:
763:
759:
743:
740:
733:
731:
728:
725:
724:
718:
715:
708:
706:
703:
700:
699:
693:
691:4,294,967,296
690:
683:
681:
678:
675:
674:
670:
667:
664:
662:
659:
656:
655:
651:
648:
645:
643:
640:
637:
636:
632:
629:
626:
624:
621:
618:
617:
613:
610:
607:
604:
602:98.09 dB
601:
598:
597:
593:
590:
587:
585:83.04 dB
584:
582:74.01 dB
581:
578:
577:
573:
570:
567:
565:77.01 dB
564:
562:67.99 dB
561:
558:
557:
554:β128 to +127
553:
550:
547:
545:58.92 dB
544:
542:49.93 dB
541:
538:
537:
533:
530:
528:1.723 dB
527:
525:34.31 dB
524:
522:25.84 dB
521:
518:
517:
511:
509:(per sample)
506:
502:(quantization
497:
488:
479:
476:
475:
469:
467:
463:
459:
455:
451:
446:
444:
440:
421:
407:
403:
400:
397:
391:
383:
379:
375:
370:
362:
357:
353:
349:
346:
334:
333:
332:
330:
326:
307:
304:
299:
285:
281:
276:
272:
270:
266:
263:(ADC) can be
262:
257:
255:
251:
247:
243:
233:
231:
227:
223:
219:
214:
210:
206:
202:
197:
195:
191:
186:
184:
180:
176:
171:
170:exponentially
166:
164:
160:
156:
155:binary number
152:
148:
144:
140:
139:analog signal
137:the original
136:
126:
124:
120:
115:
113:
109:
105:
104:noise shaping
101:
97:
96:dynamic range
93:
89:
84:
82:
78:
74:
70:
66:
62:
58:
54:
50:
49:digital audio
41:
37:
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