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Pulse-code modulation (PCM) is a method used to digitally represent sampled
analog signal An analog signal or analogue signal (see spelling differences) is any continuous signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies ...
s. It is the standard form of digital audio in computers,
compact disc The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in October ...
s,
digital telephony Telephony ( ) is the field of technology involving the development, application, and deployment of telecommunication services for the purpose of electronic transmission of voice, fax, or data, between distant parties. The history of telephony is i ...
and other digital audio applications. In a PCM stream, the
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of a ...
of the analog signal is
sampled Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of so ...
regularly at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which quantization levels vary as a function of amplitude (as with the
A-law algorithm An A-law algorithm is a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, i.e. modify, the dynamic range of an analog signal for digitizing. It is one of two versions of the G.711 standard ...
or the
μ-law algorithm The μ-law algorithm (sometimes written mu-law, often approximated as u-law) is a companding algorithm, primarily used in 8-bit PCM digital telecommunication systems in North America and Japan. It is one of two versions of the G.711 stand ...
). 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 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 spa ...
, 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 Multiplex may refer to: * Multiplex (automobile), a former American car make * Multiplex (comics), a DC comic book supervillain * Multiplex (company), a global contracting and development company * Multiplex (assay), a biological assay which meas ...
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 In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...
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. In 1926, Paul M. Rainey of
Western Electric The Western Electric Company was an American electrical engineering and manufacturing company officially founded in 1869. A wholly owned subsidiary of American Telephone & Telegraph for most of its lifespan, it served as the primary equipment m ...
patented a facsimile machine which transmitted its signal using 5-bit PCM, encoded by an opto-mechanical
analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) 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 provid ...
. The machine did not go into production. 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 ITT Inc., formerly ITT Corporation, is an American worldwide manufacturing company based in Stamford, Connecticut. The company produces specialty components for the aerospace, transportation, energy and industrial markets. ITT's three business ...
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. By this time Reeves had started working at the
Telecommunications Research Establishment The Telecommunications Research Establishment (TRE) was the main United Kingdom research and development organization for radio navigation, radar, infra-red detection for heat seeking missiles, and related work for the Royal Air Force (RAF) d ...
. The first transmission of
speech Speech is a human vocal communication using language. Each language uses phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound different from all French words, even if they are th ...
by digital techniques, the
SIGSALY SIGSALY (also known as the X System, Project X, Ciphony I, and the Green Hornet) was a secure speech system used in World War II for the highest-level Allied communications. It pioneered a number of digital communications concepts, including th ...
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 DATAR, short for ''Digital Automated Tracking and Resolving'', was a pioneering computerized battlefield information system. DATAR combined the data from all of the sensors in a naval task force into a single "overall view" that was then transmi ...
system, Ferranti Canada built a working PCM radio system that was able to transmit digitized radar data over long distances. PCM in the late 1940s and early 1950s used a cathode-ray coding tube with a
plate electrode A plate, usually called anode in Britain, is a type of electrode that forms part of a vacuum tube. It is usually made of sheet metal, connected to a wire which passes through the glass envelope of the tube to a terminal in the base of the tu ...
having encoding perforations. As in an
oscilloscope An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
, 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 The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representa ...
and produced all bits simultaneously by using a fan beam instead of a scanning beam. In the United States, the
National Inventors Hall of Fame The National Inventors Hall of Fame (NIHF) is an American not-for-profit organization, founded in 1973, which recognizes individual engineers and inventors who hold a U.S. patent of significant technology. Besides the Hall of Fame, it also ope ...
has honored Bernard M. Oliver and Claude Shannon as the inventors of PCM, as described in "Communication System Employing Pulse Code Modulation", 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: . The three of them published "The Philosophy of PCM" in 1948. The
T-carrier The T-carrier is a member of the series of carrier systems developed by AT&T Bell Laboratories for digital transmission of multiplexed telephone calls. The first version, the Transmission System 1 (T1), was introduced in 1962 in the Bell ...
system, introduced in 1961, uses two twisted-pair transmission lines to carry 24 PCM
telephone A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into ...
calls sampled at 8 kHz and 8-bit resolution. This development improved capacity and call quality compared to the previous
frequency-division multiplexing In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separat ...
schemes. In 1973,
adaptive differential pulse-code modulation 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 rat ...
(ADPCM) was developed, by P. Cummiskey, Nikil Jayant and James L. Flanagan.

## Digital audio recordings

In 1967, the first PCM recorder was developed by
NHK , also known as NHK, is a Japanese public broadcaster. NHK, which has always been known by this romanized initialism in Japanese, is a statutory corporation funded by viewers' payments of a television license fee. NHK operates two terrestri ...
's research facilities in Japan. The 30 kHz 12-bit device used a
compander In telecommunication and signal processing, companding (occasionally called compansion) is a method of mitigating the detrimental effects of a channel with limited dynamic range. The name is a portmanteau of the words compressing and expanding, ...
(similar to DBX Noise Reduction) to extend the dynamic range, and stored the signals on a
video tape recorder A video tape recorder (VTR) is a tape recorder designed to record and playback video and audio material from magnetic tape. The early VTRs were open-reel devices that record on individual reels of 2-inch-wide (5.08 cm) tape. They were ...
. In 1969, NHK expanded the system's capabilities to 2-channel
stereo Stereophonic sound, or more commonly stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible perspective. This is usually achieved by using two independent audio channels through a configuration ...
and 32 kHz 13-bit resolution. In January 1971, using NHK's PCM recording system, engineers at
Denon is a Japanese electronics company started in 1910 by Frederick Whitney Horn, an American entrepreneur. Denon produced the first cylinder audio media in Japan and players to play them. Decades later, Denon was involved in the early stages of de ...
recorded the first commercial digital recordings.Among the first recordings was ''Uzu: The World Of Stomu Yamash'ta 2'' by
Stomu Yamashta Stomu Yamashta (or Yamash'ta), born , is a Japanese percussionist, keyboardist and composer. He is best known for pioneering and popularising a fusion of traditional Japanese percussive music with Western progressive rock music in the 1960s and 1 ...
.
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.The first recording with this new system was recorded in
Tokyo Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, with an estimated 37.46 ...
during April 24–26, 1972.
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 Emphasis or emphatic may refer to: Communication * Emphasis (telecommunications), intentional alteration of the amplitude-vs.-frequency characteristics of the signal meant to reduce adverse effects of noise * Cultural emphasis, alleged tendency ...
, making it equivalent to 15.5 bits." 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. The
compact disc The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in October ...
(CD) brought PCM to consumer audio applications with its introduction in 1982. The CD uses a
44,100 Hz In digital audio, 44,100  Hz (alternately represented as 44.1 kHz) is a common sampling frequency. Analog audio is often recorded by sampling it 44,100 times per second, and then these samples are used to reconstruct the audio signal w ...
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 Telephony ( ) is the field of technology involving the development, application, and deployment of telecommunication services for the purpose of electronic transmission of voice, fax, or data, between distant parties. The history of telephony is i ...
was enabled by
metal–oxide–semiconductor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which ...
(MOS) switched capacitor (SC) circuit technology, developed in the early 1970s. This led to the development of PCM codec-filter chips in the late 1970s. The
silicon-gate In semiconductor electronics fabrication technology, a self-aligned gate is a transistor manufacturing approach whereby the gate electrode of a MOSFET (metal–oxide–semiconductor field-effect transistor) is used as a mask for the doping of th ...
CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSF ...
(complementary MOS) PCM codec-filter chip, developed by David A. Hodges and W.C. Black in 1980, has since been the industry standard for digital telephony. By the 1990s,
telecommunication network A telecommunications network is a group of nodes interconnected by telecommunications links that are used to exchange messages between the nodes. The links may use a variety of technologies based on the methodologies of circuit switching, messa ...
s such as the public switched telephone network (PSTN) had been largely
digitized DigitizationTech Target. (2011, April). Definition: digitization. ''WhatIs.com''. Retrieved December 15, 2021, from https://whatis.techtarget.com/definition/digitization is the process of converting information into a digital (i.e. computer- ...
with
very-large-scale integration Very large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining millions or billions of MOS transistors onto a single chip. VLSI began in the 1970s when MOS integrated circuit (Metal Oxide Semiconductor) c ...
(VLSI) CMOS PCM codec-filters, widely used in electronic switching systems for telephone exchanges, user-end
modems A modulator-demodulator or modem is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by modulating one or more car ...
and a wide range of
digital transmission Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
applications such as the
integrated services digital network Integrated Services Digital Network (ISDN) is a set of communication standards for simultaneous digital transmission of voice, video, data, and other network services over the digitalised circuits of the public switched telephone network. W ...
(ISDN), cordless telephones and
cell phones A mobile phone, cellular phone, cell phone, cellphone, handphone, hand phone or pocket phone, sometimes shortened to simply mobile, cell, or just phone, is a portable telephone that can make and receive calls over a radio frequency link whil ...
.

# Implementations

PCM is the method of encoding typically used for uncompressed digital audio.Other methods exist such as
pulse-density modulation 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- ...
used also on Super Audio CD.
* The
4ESS switch The No. 4 Electronic Switching System (4ESS) is a class 4 telephone electronic switching system that was the first digital electronic toll switch introduced by Western Electric for long-distance switching. It was introduced in Chicago in January ...
introduced time-division switching into the US telephone system in 1976, based on medium scale integrated circuit technology. * LPCM is used for the lossless encoding of audio data in the compact disc Red Book standard (informally also known as ''Audio CD''), introduced in 1982. *
AES3 AES3 is a standard for the exchange of digital audio signals between professional audio devices. An AES3 signal can carry two channels of pulse-code-modulated digital audio over several transmission media including balanced lines, unbalanced ...
(specified in 1985, upon which
S/PDIF S/PDIF (Sony/Philips Digital Interface) is a type of digital audio interface used in consumer audio equipment to output audio over relatively short distances. The signal is transmitted over either a coaxial cable (using RCA or BNC connecto ...
is based) is a particular format using LPCM. *
LaserDisc The LaserDisc (LD) is a home video format and the first commercial optical disc storage medium, initially licensed, sold and marketed as MCA DiscoVision (also known simply as "DiscoVision") in the United States in 1978. Its diameter typical ...
s with digital sound have an LPCM track on the digital channel. * On PCs, PCM and LPCM often refer to the format used in WAV (defined in 1991) and
AIFF Audio Interchange File Format (AIFF) is an audio file format standard used for storing sound data for personal computers and other electronic audio devices. The format was developed by Apple Inc. in 1988 based on Electronic Arts' Interchange File ...
audio container formats (defined in 1988). LPCM data may also be stored in other formats such as AU, raw audio format (header-less file) and various multimedia container formats. * LPCM has been defined as a part of the
DVD The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any ki ...
(since 1995) and
Blu-ray The Blu-ray Disc (BD), often known simply as Blu-ray, is a digital optical disc data storage format. It was invented and developed in 2005 and released on June 20, 2006 worldwide. It is designed to supersede the DVD format, and capable of st ...
(since 2006) standards. It is also defined as a part of various digital video and audio storage formats (e.g. DV since 1995,
AVCHD AVCHD (Advanced Video Coding High Definition) is a file-based format for the digital recording and playback of high-definition video. It is H.264 and Dolby AC-3 packaged into the MPEG transport stream, with a set of constraints designed around ...
since 2006). * LPCM is used by
HDMI High-Definition Multimedia Interface (HDMI) is a proprietary audio/video interface for transmitting uncompressed video data and compressed or uncompressed digital audio data from an HDMI-compliant source device, such as a display controll ...
(defined in 2002), a single-cable digital audio/video connector interface for transmitting uncompressed digital data. * RF64 container format (defined in 2007) uses LPCM and also allows non-PCM bitstream storage: various compression formats contained in the RF64 file as data bursts (Dolby E, Dolby AC3, DTS, MPEG-1/MPEG-2 Audio) can be "disguised" as PCM linear.

# Modulation

In the diagram, a
sine wave A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...
(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 In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) 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 provid ...
(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 In connection-oriented communication, a data stream is the transmission of a sequence of digitally encoded coherent signals to convey information. Typically, the transmitted symbols are grouped into a series of packets. Data streaming has ...
, 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 converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archi ...
s (DACs). They produce a
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
or
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
(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 In a mixed-signal system ( analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter ( DAC) or other sam ...
that suppresses energy outside the expected frequency range (greater than the
Nyquist frequency In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), ...
$f_s / 2$).Some systems use
digital filter In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filte ...
ing 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 An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruc ...
is much simpler. In some systems, no explicit filtering is done at all; as it's 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.

# Standard sampling precision and rates

Common sample depths for LPCM are 8, 16, 20 or 24 bits per sample. LPCM encodes a single sound channel. Support for multichannel audio depends on file format and relies on synchronization of multiple LPCM streams. While two channels (stereo) is the most common format, systems can support up to 8 audio channels (7.1 surround) or more. Common sampling frequencies are 48 kHz as used with
DVD The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any ki ...
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.

# 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 A voice frequency (VF) or voice band is the range of audio frequencies used for the transmission of speech. Frequency band In telephony, the usable voice frequency band ranges from approximately 300 to 3400  Hz. It is for this reason ...
band ranges from approximately 300  Hz to 3400 Hz. 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: * Choosing a discrete value that is near but not exactly at the analog signal level for each sample leads to
quantization error Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and ...
.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 ''q''2/12. * Between samples no measurement of the signal is made; the sampling theorem guarantees non-ambiguous representation and recovery of the signal only if it has no energy at frequency ''fs''/2 or higher (one half the sampling frequency, known as the
Nyquist frequency In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), ...
); higher frequencies will not be correctly represented or recovered and add aliasing distortion to the signal below the Nyquist frequency. * As samples are dependent on time, an accurate clock is required for accurate reproduction. If either the encoding or decoding clock is not stable, these imperfections will directly affect the output quality of the device.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 In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a signifi ...
, however.

# 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 The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where ...
(MDCT) coding. * Linear PCM (LPCM) is PCM with linear quantization. * Differential PCM (DPCM) encodes the PCM values as differences between the current and the predicted value. An algorithm predicts the next sample based on the previous samples, and the encoder stores only the difference between this prediction and the actual value. If the prediction is reasonable, fewer bits can be used to represent the same information. For audio, this type of encoding reduces the number of bits required per sample by about 25% compared to PCM. *
Adaptive differential pulse-code modulation 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 rat ...
(ADPCM) is a variant of DPCM that varies the size of the quantization step, to allow further reduction of the required bandwidth for a given
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in d ...
. *
Delta modulation A delta modulation (DM or Δ-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 puls ...
is a form of DPCM that uses one bit per sample to indicate whether the signal is increasing or decreasing compared to the previous sample. 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 Digital Signal 0 (DS0) is a basic digital signaling rate of 64 kilobits per second (kbit/s), corresponding to the capacity of one analog voice-frequency-equivalent communication channel. The DS0 rate, and its equivalents E0 in the E-carrier system ...
. The default signal compression encoding on a DS0 is either μ-law (mu-law) PCM (North America and Japan) or
A-law An A-law algorithm is a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, i.e. modify, the dynamic range of an analog signal for digitizing. It is one of two versions of the G.711 stand ...
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 G.711 is a narrowband audio codec originally designed for use in telephony that provides toll-quality audio at 64 kbit/s. G.711 passes audio signals in the range of 300–3400 Hz and samples them at the rate of 8,000 samples per second ...
. 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 An audio codec is a device or computer program capable of encoding or decoding a digital data stream (a codec) that encodes or decodes audio. In software, an audio codec is a computer program implementing an algorithm that compresses and decompres ...
have been developed to achieve further compression. Some of these techniques have been standardized and patented. Advanced compression techniques, such as MDCT and linear predictive coding (LPC), are now widely used in mobile phones,
voice over IP Voice over Internet Protocol (VoIP), also called IP telephony, is a method and group of technologies for the delivery of voice communications and multimedia sessions over Internet Protocol (IP) networks, such as the Internet. The terms Internet ...
(VoIP) and
streaming media Streaming media is multimedia that is delivered and consumed in a continuous manner from a source, with little or no intermediate storage in network elements. ''Streaming'' refers to the delivery method of content, rather than the content it ...
.

# Encoding for serial transmission

PCM can be either
return-to-zero Return-to-zero (RZ or RTZ) describes a line code used in telecommunications signals in which the signal drops (returns) to zero between each pulse. This takes place even if a number of consecutive 0s or 1s occur in the signal. The signal is ...
(RZ) or
non-return-to-zero In telecommunication, a non-return-to-zero (NRZ) line code is a binary code in which ones are represented by one significant condition, usually a positive voltage, while zeros are represented by some other significant condition, usually a negat ...
(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''.Stallings, William
Digital Signaling Techniques
December 1984, Vol. 22, No. 12, IEEE Communications Magazine
Ones-density is often controlled using precoding techniques such as
run-length limited Run-length limited or RLL coding is a line coding technique that is used to send arbitrary data over a communications channel with bandwidth limits. RLL codes are defined by four main parameters: ''m'', ''n'', ''d'', ''k''. The first two, ''m ...
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 In telecommunications, a scrambler is a device that transposes or inverts signals or otherwise encodes a message at the sender's side to make the message unintelligible at a receiver not equipped with an appropriately set descrambling device. Whe ...
on the data, which will tend to turn the data stream into a stream that looks
pseudo-random A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Background The generation of random numbers has many uses, such as for rando ...
, 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 In signal processing, when describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean amplitude of the waveform. If the mean amplitude is zero, there is no DC bias. A waveform with n ...
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 In telecommunication, bipolar encoding is a type of return-to-zero (RZ) line code, where two nonzero values are used, so that the three values are +, −, and zero. Such a signal is called a duobinary signal. Standard bipolar encodings are designe ...
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 Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of voltage (and current) fed ...
and
pulse-position modulation Pulse-position modulation (PPM) is a form of signal modulation in which ''M'' message bits are encoded by transmitting a single pulse in one of 2^M possible required time shifts. This is repeated every ''T'' seconds, such that the transmitted bi ...
, in which the information to be encoded is represented by discrete signal pulses of varying width or position, respectively. 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.

* Beta encoder * Equivalent pulse code modulation noise * Signal-to-quantization-noise ratio (SQNR), one method of measuring quantization error

# References

* * * * *

PCM description on MultimediaWiki

Ralph Miller
and Bob Badgley invented multi-level PCM independently in their work at Bell Labs on
SIGSALY SIGSALY (also known as the X System, Project X, Ciphony I, and the Green Hornet) was a secure speech system used in World War II for the highest-level Allied communications. It pioneered a number of digital communications concepts, including th ...
: filed in 1943: N-ary Pulse Code Modulation.