Pulse-code modulation

Last updated

Pulse-code modulation
Filename extension
.L16, .WAV, .AIFF, .AU, .PCM [1]
Internet media type
audio/L16, audio/L8, [2] audio/L20, audio/L24 [3] [4]
Type code "AIFF" for L16, [1] none [3]
Magic number Varies
Type of formatUncompressed audio
Contained by Audio CD, AES3, WAV, AIFF, AU, M2TS, VOB, and many others
Open format?Yes
Free format?Yes [5]

Pulse-code modulation (PCM) is a method used to digitally represent analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Alec Reeves, Claude Shannon, Barney Oliver and John R. Pierce are credited with its invention. [6] [7] [8]

Contents

Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform. [5] This is in contrast to PCM encodings in which quantization levels vary as a function of amplitude (as with the A-law algorithm or the μ-law algorithm). Though PCM is a more general term, it is often used to describe data encoded as LPCM.

A PCM stream has two basic properties that determine the stream's fidelity to the original analog signal: the sampling rate, which is the number of times per second that samples are taken; and the bit depth, which determines the number of possible digital values that can be used to represent each sample.

History

Early electrical communications started to sample signals in order to multiplex samples from multiple telegraphy sources and to convey them over a single telegraph cable. The American inventor Moses G. Farmer conceived telegraph time-division multiplexing (TDM) as early as 1853. Electrical engineer W. M. Miner, in 1903, used an electro-mechanical commutator for time-division multiplexing multiple telegraph signals; he also applied this technology to telephony. He obtained intelligible speech from channels sampled at a rate above 3500–4300 Hz; lower rates proved unsatisfactory.

In 1920, the Bartlane cable picture transmission system used telegraph signaling of characters punched in paper tape to send samples of images quantized to 5 levels. [9] In 1926, Paul M. Rainey of Western Electric patented a facsimile machine that transmitted its signal using 5-bit PCM, encoded by an opto-mechanical analog-to-digital converter. [10] The machine did not go into production. [11]

British engineer Alec Reeves, unaware of previous work, conceived the use of PCM for voice communication in 1937 while working for International Telephone and Telegraph in France. He described the theory and its advantages, but no practical application resulted. Reeves filed for a French patent in 1938, and his US patent was granted in 1943. [12] By this time Reeves had started working at the Telecommunications Research Establishment. [11]

The first transmission of speech by digital techniques, the SIGSALY encryption equipment, conveyed high-level Allied communications during World War II. In 1943 the Bell Labs researchers who designed the SIGSALY system became aware of the use of PCM binary coding as already proposed by Reeves. In 1949, for the Canadian Navy's DATAR system, Ferranti Canada built a working PCM radio system that was able to transmit digitized radar data over long distances. [13]

PCM in the late 1940s and early 1950s used a cathode-ray coding tube with a plate electrode having encoding perforations. [14] As in an oscilloscope, the beam was swept horizontally at the sample rate while the vertical deflection was controlled by the input analog signal, causing the beam to pass through higher or lower portions of the perforated plate. The plate collected or passed the beam, producing current variations in binary code, one bit at a time. Rather than natural binary, the grid of Goodall's later tube was perforated to produce a glitch-free Gray code and produced all bits simultaneously by using a fan beam instead of a scanning beam. [15]

In the United States, the National Inventors Hall of Fame has honored Bernard M. Oliver [16] and Claude Shannon [17] as the inventors of PCM, [18] as described in "Communication System Employing Pulse Code Modulation", U.S. patent 2,801,281 filed in 1946 and 1952, granted in 1956. Another patent by the same title was filed by John R. Pierce in 1945, and issued in 1948: U.S. patent 2,437,707 . The three of them published "The Philosophy of PCM" in 1948. [19]

The T-carrier system, introduced in 1961, uses two twisted-pair transmission lines to carry 24 PCM telephone calls sampled at 8 kHz and 8-bit resolution. This development improved capacity and call quality compared to the previous frequency-division multiplexing schemes.

In 1973, adaptive differential pulse-code modulation (ADPCM) was developed, by P. Cummiskey, Nikil Jayant and James L. Flanagan. [20]

Digital audio recordings

In 1967, the first PCM recorder was developed by NHK's research facilities in Japan. [21] The 30 kHz 12-bit device used a compander (similar to DBX Noise Reduction) to extend the dynamic range, and stored the signals on a video tape recorder. In 1969, NHK expanded the system's capabilities to 2-channel stereo and 32 kHz 13-bit resolution. In January 1971, using NHK's PCM recording system, engineers at Denon recorded the first commercial digital recordings. [note 1] [21]

In 1972, Denon unveiled the first 8-channel digital recorder, the DN-023R, which used a 4-head open reel broadcast video tape recorder to record in 47.25 kHz, 13-bit PCM audio. [note 2] In 1977, Denon developed the portable PCM recording system, the DN-034R. Like the DN-023R, it recorded 8 channels at 47.25 kHz, but it used 14-bits "with emphasis, making it equivalent to 15.5 bits." [21]

In 1979, the first digital pop album, Bop till You Drop, was recorded. It was recorded in 50 kHz, 16-bit linear PCM using a 3M digital tape recorder. [22]

The compact disc (CD) brought PCM to consumer audio applications with its introduction in 1982. The CD uses a 44,100 Hz sampling frequency and 16-bit resolution and stores up to 80 minutes of stereo audio per disc.

Digital telephony

The rapid development and wide adoption of PCM digital telephony was enabled by metal–oxide–semiconductor (MOS) switched capacitor (SC) circuit technology, developed in the early 1970s. [23] This led to the development of PCM codec-filter chips in the late 1970s. [23] [24] The silicon-gate CMOS (complementary MOS) PCM codec-filter chip, developed by David A. Hodges and W.C. Black in 1980, [23] has since been the industry standard for digital telephony. [23] [24] By the 1990s, telecommunication networks such as the public switched telephone network (PSTN) had been largely digitized with very-large-scale integration (VLSI) CMOS PCM codec-filters, widely used in electronic switching systems for telephone exchanges, user-end modems and a wide range of digital transmission applications such as the integrated services digital network (ISDN), cordless telephones and cell phones. [24]

Implementations

PCM is the method of encoding typically used for uncompressed digital audio. [note 3]

Modulation

Sampling and quantization of a signal (red) for 4-bit LPCM over a time domain at specific frequency Pcm.svg
Sampling and quantization of a signal (red) for 4-bit LPCM over a time domain at specific frequency

In the diagram, a sine wave (red curve) is sampled and quantized for PCM. The sine wave is sampled at regular intervals, shown as vertical lines. For each sample, one of the available values (on the y-axis) is chosen. The PCM process is commonly implemented on a single integrated circuit called an analog-to-digital converter (ADC). This produces a fully discrete representation of the input signal (blue points) that can be easily encoded as digital data for storage or manipulation. Several PCM streams could also be multiplexed into a larger aggregate data stream, generally for transmission of multiple streams over a single physical link. One technique is called time-division multiplexing (TDM) and is widely used, notably in the modern public telephone system.

Demodulation

The electronics involved in producing an accurate analog signal from the discrete data are similar to those used for generating the digital signal. These devices are digital-to-analog converters (DACs). They produce a voltage or current (depending on type) that represents the value presented on their digital inputs. This output would then generally be filtered and amplified for use.

To recover the original signal from the sampled data, a demodulator can apply the procedure of modulation in reverse. After each sampling period, the demodulator reads the next value and transitions the output signal to the new value. As a result of these transitions, the signal retains a significant amount of high-frequency energy due to imaging effects. To remove these undesirable frequencies, the demodulator passes the signal through a reconstruction filter that suppresses energy outside the expected frequency range (greater than the Nyquist frequency ). [note 4]

Standard sampling precision and rates

Common sample depths for LPCM are 8, 16, 20 or 24 bits per sample. [1] [2] [3] [32]

LPCM encodes a single sound channel. Support for multichannel audio depends on file format and relies on synchronization of multiple LPCM streams. [5] [33] While two channels (stereo) is the most common format, systems can support up to 8 audio channels (7.1 surround) [2] [3] or more.

Common sampling frequencies are 48 kHz as used with DVD format videos, or 44.1 kHz as used in CDs. Sampling frequencies of 96 kHz or 192 kHz can be used on some equipment, but the benefits have been debated. [34]

Limitations

The Nyquist–Shannon sampling theorem shows PCM devices can operate without introducing distortions within their designed frequency bands if they provide a sampling frequency at least twice that of the highest frequency contained in the input signal. For example, in telephony, the usable voice frequency band ranges from approximately 300  Hz to 3400 Hz. [35] For effective reconstruction of the voice signal, telephony applications therefore typically use an 8000 Hz sampling frequency which is more than twice the highest usable voice frequency.

Regardless, there are potential sources of impairment implicit in any PCM system:

Processing and coding

Some forms of PCM combine signal processing with coding. Older versions of these systems applied the processing in the analog domain as part of the analog-to-digital process; newer implementations do so in the digital domain. These simple techniques have been largely rendered obsolete by modern transform-based audio compression techniques, such as modified discrete cosine transform (MDCT) coding.

In telephony, a standard audio signal for a single phone call is encoded as 8,000 samples per second, of 8 bits each, giving a 64 kbit/s digital signal known as DS0. The default signal compression encoding on a DS0 is either μ-law (mu-law) PCM (North America and Japan) or A-law PCM (Europe and most of the rest of the world). These are logarithmic compression systems where a 12- or 13-bit linear PCM sample number is mapped into an 8-bit value. This system is described by international standard G.711.

Where circuit costs are high and loss of voice quality is acceptable, it sometimes makes sense to compress the voice signal even further. An ADPCM algorithm is used to map a series of 8-bit μ-law or A-law PCM samples into a series of 4-bit ADPCM samples. In this way, the capacity of the line is doubled. The technique is detailed in the G.726 standard.

Audio coding formats and audio codecs have been developed to achieve further compression. Some of these techniques have been standardized and patented. Advanced compression techniques, such as modified discrete cosine transform (MDCT) and linear predictive coding (LPC), are now widely used in mobile phones, voice over IP (VoIP) and streaming media.

Encoding for serial transmission

PCM can be either return-to-zero (RZ) or non-return-to-zero (NRZ). For a NRZ system to be synchronized using in-band information, there must not be long sequences of identical symbols, such as ones or zeroes. For binary PCM systems, the density of 1-symbols is called ones-density. [36]

Ones-density is often controlled using precoding techniques such as run-length limited encoding, where the PCM code is expanded into a slightly longer code with a guaranteed bound on ones-density before modulation into the channel. In other cases, extra framing bits are added into the stream, which guarantees at least occasional symbol transitions.

Another technique used to control ones-density is the use of a scrambler on the data, which will tend to turn the data stream into a stream that looks pseudo-random, but where the data can be recovered exactly by a complementary descrambler. In this case, long runs of zeroes or ones are still possible on the output but are considered unlikely enough to allow reliable synchronization.

In other cases, the long term DC value of the modulated signal is important, as building up a DC bias will tend to move communications circuits out of their operating range. In this case, special measures are taken to keep a count of the cumulative DC bias and to modify the codes if necessary to make the DC bias always tend back to zero.

Many of these codes are bipolar codes, where the pulses can be positive, negative or absent. In the typical alternate mark inversion code, non-zero pulses alternate between being positive and negative. These rules may be violated to generate special symbols used for framing or other special purposes.

Nomenclature

The word pulse in the term pulse-code modulation refers to the pulses to be found in the transmission line. This perhaps is a natural consequence of this technique having evolved alongside two analog methods, pulse-width modulation and pulse-position modulation, in which the information to be encoded is represented by discrete signal pulses of varying width or position, respectively.[ citation needed ] In this respect, PCM bears little resemblance to these other forms of signal encoding, except that all can be used in time-division multiplexing, and the numbers of the PCM codes are represented as electrical pulses.

See also

Explanatory notes

  1. ↑ Among the first recordings was Uzu: The World Of Stomu Yamash'ta 2 by Stomu Yamashta.
  2. ↑ The first recording with this new system was recorded in Tokyo during April 24–26, 1972.
  3. ↑ Other methods exist such as pulse-density modulation used also on Super Audio CD.
  4. ↑ Some systems use digital filtering to remove some of the aliasing, converting the signal from digital to analog at a higher sample rate such that the analog anti-aliasing filter is much simpler. In some systems, no explicit filtering is done at all; as it is impossible for any system to reproduce a signal with infinite bandwidth, inherent losses in the system compensate for the artifacts — or the system simply does not require much precision.
  5. ↑ Quantization error swings between -q/2 and q/2. In the ideal case (with a fully linear ADC and signal level >> q) it is uniformly distributed over this interval, with zero mean and variance of q2/12.
  6. ↑ A slight difference between the encoding and decoding clock frequencies is not generally a major concern; a small constant error is not noticeable. Clock error does become a major issue if the clock contains significant jitter, however.

Related Research Articles

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a separate signal called the modulation signal that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer.

<span class="mw-page-title-main">Analog-to-digital converter</span> System that converts an analog signal into a digital signal

In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

<span class="mw-page-title-main">Delta modulation</span> Signal conversion technique

Delta modulation is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation (DPCM) where the difference between successive samples is encoded into n-bit data streams. In delta modulation, the transmitted data are reduced to a 1-bit data stream representing either up (↗) or down (↘). Its main features are:

<span class="mw-page-title-main">Digital audio</span> Technology that records, stores, and reproduces sound

Digital audio is a representation of sound recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical samples in a continuous sequence. For example, in CD audio, samples are taken 44,100 times per second, each with 16-bit resolution. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form. Following significant advances in digital audio technology during the 1970s and 1980s, it gradually replaced analog audio technology in many areas of audio engineering, record production and telecommunications in the 1990s and 2000s.

<span class="mw-page-title-main">G.711</span> ITU-T recommendation

G.711 is a narrowband audio codec originally designed for use in telephony that provides toll-quality audio at 64 kbit/s. It is an ITU-T standard (Recommendation) for audio encoding, titled Pulse code modulation (PCM) of voice frequencies released for use in 1972.

Sound can be recorded and stored and played using either digital or analog techniques. Both techniques introduce errors and distortions in the sound, and these methods can be systematically compared. Musicians and listeners have argued over the superiority of digital versus analog sound recordings. Arguments for analog systems include the absence of fundamental error mechanisms which are present in digital audio systems, including aliasing and associated anti-aliasing filter implementation, jitter and quantization noise. Advocates of digital point to the high levels of performance possible with digital audio, including excellent linearity in the audible band and low levels of noise and distortion.

<span class="mw-page-title-main">Sampling (signal processing)</span> Measurement of a signal at discrete time intervals

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values.

<span class="mw-page-title-main">Sound quality</span> Assessment of the audio output from an electronic device

Sound quality is typically an assessment of the accuracy, fidelity, or intelligibility of audio output from an electronic device. Quality can be measured objectively, such as when tools are used to gauge the accuracy with which the device reproduces an original sound; or it can be measured subjectively, such as when human listeners respond to the sound or gauge its perceived similarity to another sound.

<span class="mw-page-title-main">Direct Stream Digital</span> System for digitally encoding audio signals

Direct Stream Digital (DSD) is a trademark used by Sony and Philips for their system for digitally encoding audio signals for the Super Audio CD (SACD).

<span class="mw-page-title-main">Digital recording</span> Audio or video represented as a stream of discrete numbers

In digital recording, an audio or video signal is converted into a stream of discrete numbers representing the changes over time in air pressure for audio, or chroma and luminance values for video. This number stream is saved to a storage device. To play back a digital recording, the numbers are retrieved and converted back into their original analog audio or video forms so that they can be heard or seen.

<span class="mw-page-title-main">Secure voice</span> Encrypted voice communication

Secure voice is a term in cryptography for the encryption of voice communication over a range of communication types such as radio, telephone or IP.

<span class="mw-page-title-main">Delta-sigma modulation</span> Method for converting signals between digital and analog

Delta-sigma modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency as part of the process of delta-sigma analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Delta-sigma modulation achieves high quality by utilizing a negative feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies well above the original signal's bandwidth. Subsequent low-pass filtering for demodulation easily removes this high frequency noise and time averages to achieve high accuracy in amplitude which can be ultimately encoded as pulse-code modulation (PCM).

<span class="mw-page-title-main">PCM adaptor</span> Encodes digital audio as video

A PCM adaptor is a device that encodes digital audio as video for recording on a videocassette recorder. The adapter also has the ability to decode a video signal back to digital audio for playback. This digital audio system was used for mastering early compact discs.

The dbx Model 700 Digital Audio Processor was a professional audio ADC/DAC combination unit, which digitized a stereo analog audio input into a bitstream, which was then encoded and encapsulated in an analog composite video signal, for recording to tape using a VCR as a transport. Unlike other similar pieces of equipment like the Sony PCM-F1, the Model 700 used a technique called Companded Predictive Delta Modulation, rather than the now-common pulse-code modulation. At the time of its introduction in the mid-1980s the device was the first commercial product to use this method, although it had been proposed in the 1960s and prototyped in the late '70s.

<span class="mw-page-title-main">Audio bit depth</span> Number of bits of information recorded for each digital audio sample

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.

Adaptive differential pulse-code modulation (ADPCM) is a variant of differential pulse-code modulation (DPCM) that varies the size of the quantization step, to allow further reduction of the required data bandwidth for a given signal-to-noise ratio.

<span class="mw-page-title-main">Sub-band coding</span>

In signal processing, sub-band coding (SBC) is any form of transform coding that breaks a signal into a number of different frequency bands, typically by using a fast Fourier transform, and encodes each one independently. This decomposition is often the first step in data compression for audio and video signals.

The pulse-code modulation (PCM) technology was patented and developed in France in 1938, but could not be used because suitable technology was not available until World War II. This came about with the arrival of digital systems in the 1960s when improving the performance of communications networks became a real possibility. However, this technology was not completely adopted until the mid-1970s, due to the large amount of analog systems already in place and the high cost of digital systems, as semiconductors were very expensive. PCM's initial goal was to convert an analog voice telephone channel into a digital one based on the sampling theorem.

Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with a binary signal. In a PDM signal, specific amplitude values are not encoded into codewords of pulses of different weight as they would be in pulse-code modulation (PCM); rather, the relative density of the pulses corresponds to the analog signal's amplitude. The output of a 1-bit DAC is the same as the PDM encoding of the signal.

References

  1. 1 2 3 Alvestrand, Harald Tveit; Salsman, James (May 1999). "RFC 2586 – The Audio/L16 MIME content type". The Internet Society. doi:10.17487/RFC2586 . Retrieved March 16, 2010.{{cite journal}}: Cite journal requires |journal= (help)
  2. 1 2 3 Casner, S. (March 2007). "RFC 4856 – Media Type Registration of Payload Formats in the RTP Profile for Audio and Video Conferences – Registration of Media Type audio/L8". The IETF Trust. doi:10.17487/RFC4856 . Retrieved March 16, 2010.{{cite journal}}: Cite journal requires |journal= (help)
  3. 1 2 3 4 Bormann, C.; Casner, S.; Kobayashi, K.; Ogawa, A. (January 2002). "RFC 3190 – RTP Payload Format for 12-bit DAT Audio and 20- and 24-bit Linear Sampled Audio". The Internet Society. doi: 10.17487/RFC3190 . Retrieved March 16, 2010.{{cite journal}}: Cite journal requires |journal= (help)
  4. ↑ "Audio Media Types". Internet Assigned Numbers Authority. Retrieved March 16, 2010.
  5. 1 2 3 4 "Linear Pulse Code Modulated Audio (LPCM)". Library of Congress. April 19, 2022. Retrieved September 5, 2022.
  6. ↑ Noll, A. Michael (1997). Highway of Dreams: A Critical View Along the Information Superhighway. Telecommunications (Revised ed.). Mahwah, NJ: Erlbaum. p. 50. ISBN   978-0-8058-2557-2.
  7. ↑ Leibson, Steven (September 7, 2021). "A Brief History of the Single-Chip DSP, Part I". EEJournal. Retrieved September 19, 2024.
  8. ↑ Barrett, G. Douglas (2023). Experimenting the Human: Art, Music, and the Contemporary Posthuman. Chicago London: The University of Chicago Press. p. 102. ISBN   978-0-226-82340-9.
  9. ↑ "The Bartlane Transmission System". DigicamHistory.com. Archived from the original on February 10, 2010. Retrieved January 7, 2010.
  10. ↑ U.S. patent number 1,608,527; also see p. 8, Data conversion handbook, Walter Allan Kester, ed., Newnes, 2005, ISBN   0-7506-7841-0.
  11. 1 2 John Vardalas (June 2013), Pulse Code Modulation: It all Started 75 Years Ago with Alec Reeves, IEEE
  12. ↑ US 2272070
  13. ↑ Porter, Arthur (2004). So Many Hills to Climb. Beckham Publications Group. ISBN   9780931761188.[ page needed ]
  14. ↑ Sears, R. W. (January 1948). Electron Beam Deflection Tube for Pulse Code Modulation. Vol. 27. Bell Labs. pp. 44–57. Retrieved May 14, 2017.{{cite book}}: |work= ignored (help)
  15. ↑ Goodall, W. M. (January 1951). Television by Pulse Code Modulation. Vol. 30. Bell Labs. pp. 33–49. Retrieved May 14, 2017.{{cite book}}: |work= ignored (help)
  16. ↑ "Bernard Oliver". National Inventor's Hall of Fame. Archived from the original on December 5, 2010. Retrieved February 6, 2011.
  17. ↑ "Claude Shannon". National Inventor's Hall of Fame. Archived from the original on December 6, 2010. Retrieved February 6, 2011.
  18. ↑ "National Inventors Hall of Fame announces 2004 class of inventors". Science Blog. February 11, 2004. Retrieved February 6, 2011.
  19. ↑ B. M. Oliver; J. R. Pierce & C. E. Shannon (November 1948). "The Philosophy of PCM". Proceedings of the IRE. 36 (11): 1324–1331. doi:10.1109/JRPROC.1948.231941. ISSN   0096-8390. S2CID   51663786.
  20. ↑ P. Cummiskey, N. S. Jayant, and J. L. Flanagan, "Adaptive quantization in differential PCM coding of speech," Bell Syst. Tech. J., vol. 52, pp. 1105–1118, Sept. 1973.
  21. 1 2 3 Thomas Fine (2008). "The dawn of commercial digital recording" (PDF). ARSC Journal . 39 (1): 1–17.
  22. ↑ Roger Nichols. "I Can't Keep Up With All The Formats II". Archived from the original on October 20, 2002. The Ry Cooder Bop Till You Drop album was the first digitally recorded pop album
  23. 1 2 3 4 Allstot, David J. (2016). "Switched Capacitor Filters" (PDF). In Maloberti, Franco; Davies, Anthony C. (eds.). A Short History of Circuits and Systems: From Green, Mobile, Pervasive Networking to Big Data Computing. IEEE Circuits and Systems Society. pp. 105–110. ISBN   9788793609860. Archived from the original (PDF) on September 30, 2021. Retrieved November 29, 2019.
  24. 1 2 3 Floyd, Michael D.; Hillman, Garth D. (October 8, 2018) [1st pub. 2000]. "Pulse-Code Modulation Codec-Filters". The Communications Handbook (2nd ed.). CRC Press. pp. 26–1, 26–2, 26–3. ISBN   9781420041163.
  25. ↑ Cambron, G. Keith (October 17, 2012). Global Networks: Engineering, Operations and Design. John Wiley & Sons. p. 345.
  26. ↑ Blu-ray Disc Association (March 2005), White paper Blu-ray Disc Format – 2.B Audio Visual Application Format Specifications for BD-ROM (PDF), retrieved July 26, 2009
  27. ↑ "DVD Technical Notes (DVD Video – "Book B") – Audio data specifications". July 21, 1996. Retrieved March 16, 2010.
  28. ↑ Jim Taylor. "DVD Frequently Asked Questions (and Answers) – Audio details of DVD-Video" . Retrieved March 20, 2010.
  29. ↑ "How DV works". Archived from the original on December 6, 2007. Retrieved March 21, 2010.
  30. ↑ "AVCHD Information Website – AVCHD format specification overview" . Retrieved March 21, 2010.
  31. ↑ EBU (July 2009), EBU Tech 3306 – MBWF / RF64: An Extended File Format for Audio (PDF), archived from the original (PDF) on November 22, 2009, retrieved January 19, 2010
  32. ↑ Mostafa, Mohamed; Kumar, Rajesh (May 2001). "RFC 3108 – Conventions for the use of the Session Description Protocol (SDP) for ATM Bearer Connections". doi:10.17487/RFC3108 . Retrieved March 16, 2010.{{cite journal}}: Cite journal requires |journal= (help)
  33. ↑ "PCM, Pulse Code Modulated Audio". Library of Congress. April 6, 2022. Retrieved September 5, 2022.
  34. ↑ Christopher, Montgometry. "24/192 Music Downloads, and why they do not make sense". Chris "Monty" Montgomery. Archived from the original on September 6, 2014. Retrieved March 16, 2013.
  35. ↑ https://www.its.bldrdoc.gov/fs-1037/dir-039/_5829.htm%5B%5D
  36. ↑ Stallings, William, Digital Signaling Techniques, December 1984, Vol. 22, No. 12, IEEE Communications Magazine

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