TheInfoList

Pulse-code modulation (PCM) is a method used to digitally represent sampled
analog signal An analog signal is any continuous signal In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time. Discrete time Discrete time views values of vari ...

s. It is the standard form of
digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical Sampling (signal processing), s ...
in computers,
compact disc The compact disc (CD) is a digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics Electronics compri ...

s,
digital telephony Telephony ( ) is the field of technology involving the development, application, and deployment of telecommunication Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usual ...
and other digital audio applications. In a PCM
stream A stream is a body of water (Lysefjord) in Norway Norway, officially the Kingdom of Norway,Names in the official and recognised languages: Bokmål Bokmål (, ; literally "book tongue") is an official written standard for the No ...
, the
amplitude The amplitude of a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Period, a descriptor for ...

of the analog signal is
sampled Sample or samples may refer to: Base meaning * Sample (statistics) In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a sci ...
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 Communication (from Latin ''communicare'', meaning "to share") is the act of developing meaning among entities or groups through th ...
or the
μ-law algorithm The μ-law algorithm (sometimes written mu-law, often approximated as u-law) is a companding After compressing, before expanding In telecommunication Telecommunication is the transmission of information Information can be thoug ...
). 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 , sampling is the reduction of a to a . A common example is the conversion of a (a continuous signal) to a sequence of samples (a discrete-time signal). A sample is a value or set of values at a point in time and/or space. A sampler is a su ...
, 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 communication or multiplexing, combining many signals into a single transmission circuit or channel ** Multi ...
samples from multiple
telegraphy Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore Flag semaphore (from the Ancient ...
sources and to convey them over a single telegraph cable. The American inventor
Moses G. Farmer Moses Gerrish Farmer (February 9, 1820 – May 25, 1893) was an electrical engineer Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, e ...
conceived telegraph
time-division multiplexing Time-division multiplexing (TDM) is a method of transmitting and receiving independent signals over a common signal path by means of synchronized switches at each end of the transmission line so that each signal appears on the line only a fractio ...
(TDM) as early as 1853. Electrical engineer W. M. Miner, in 1903, used an electro-mechanical
commutator In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gene ...
for time-division multiplexing multiple telegraph signals; he also applied this technology to
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 ...
. 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 systemBartlane cable picture transmission system was a technique invented in 1920 to transmit digitized newspaper images over submarine cable lines between London and New York. It was named after its inventors Harry G. Bartholomew and Maynard D. McFarl ...
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 Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics ...
patented a
facsimile machine Fax (short for facsimile), sometimes called telecopying or telefax (the latter short for telefacsimile), is the telephonic transmission of scanned printed material (both text and images), normally to a telephone number connected to a printer or ...
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 (signal processing), digit ...
. The machine did not go into production. British engineer
Alec Reeves Alec Harley Reeves (10 March 1902 – 13 October 1971) was a British scientist best known for his invention of pulse-code modulation Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signal An analog s ...
, 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 White Plains, New York. The company produces specialty components for the aerospace, transportation, energy and industrial markets. ITT's three busines ...
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 The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed. The Guardian' and Telegraph' u ...
. The first transmission of
speech Speech is human vocal communication Communication (from Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''c ...

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 World War II or the Second World War, often abbreviated as WWII or WW2, was a that lasted from 1939 to ...

encryption equipment, conveyed high-level Allied communications during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a global war A world war is "a war War is an intense armed conflict between states State may refer to: Arts, entertainment, and media Literatur ...
. In 1943 the
Bell Labs Nokia Bell Labs (formerly named Bell Labs Innovations (1996–2007), AT&T Bell Laboratories (1984–1996) and Bell Telephone Laboratories (1925–1984)) is an American industrial research and scientific development company A company, ab ...
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 transmit ...
system,
Ferranti Canada Ferranti-Packard Ltd. was the Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections e ...
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 Cathode rays (electron beam or e-beam) are streams of electrons observed in vacuum tube, discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow ...

coding tube with a
plate electrode The plate from an EL84 pentode tube widely used in audio amplifiers in 1960s era radios and televisions, and still used in guitar amplifiers">pentode.html" ;"title="EL84 pentode">EL84 pentode tube widely used in audio amplifiers in 1960s era radio ...
having encoding perforations. As in an
oscilloscope model 475A portable analog oscilloscope, a typical instrument of the late 1970s An oscilloscope, previously called an oscillograph, and informally known as a scope or o-scope, CRO (for cathode-ray oscilloscope), or DSO (for the more modern digit ...

, 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 just as reflected binary (RB) or Gray code after , is an ordering of the such that two successive values differ in only one (binary digit). For example, the representation of the decimal value "1" i ...

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 A nonprofit organization (NPO), also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and op ...
has honored
Bernard M. Oliver Bernard M. Oliver (May 17, 1916 – November 23, 1995), also known as Barney Oliver, was a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring kn ...
and
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbe ...
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 Labs, Bell Laboratories for digital transmission of multiplexed telephone calls. The first version, the Transmission System 1 (T1), was introduced in 1962 in the ...
system, introduced in 1961, uses two twisted-pair transmission lines to carry 24 PCM
telephone A telephone is a telecommunication Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usually cylindrical A cylinder (from Greek Greek may refer to: Greece Anyt ...

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 modulationAdaptive 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 ...
(ADPCM) was developed, by P. Cummiskey,
Nikil Jayant Nikil S. Jayant (1945 -- ) is an Indian-American communications engineer. He was a prominent long-term researcher at Bell Laboratories and subsequently a professor at Georgia Institute of Technology. He received his Ph.D. in Electrical Communication ...
and James L. Flanagan.

## Digital audio recordings

In 1967, the first PCM recorder was developed by
NHK also called the Japan Broadcasting Corporation and shortened from ''Nippon Hōsō Kyōkai'', is a Japanese government-owned public broadcaster Public broadcasting involves radio Radio is the technology of signaling and telecommunicatio ...

's research facilities in Japan. The 30 kHz 12-bit device used a
compander After compressing, before expanding In telecommunication Telecommunication is the transmission of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defi ...
(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 An audio tape recorder, also known as a tape deck, tape player or tape machine or simply a tape recorder, is a sound recording and reproduction Sound recording and reproduction is an ...
. In 1969, NHK expanded the system's capabilities to 2-channel
stereo File:Carsoundstereoshift.png, Time difference in a stereophonic recording of a car going past, 250px Stereophonic sound or, more commonly, stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible per ...

and 32 kHz 13-bit resolution. In January 1971, using NHK's PCM recording system, engineers at
Denon is a Japanese electronics Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. It uses active devices to control electron flow by amplif ...
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 Progressive rock (oft ...
.
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 (Japanese language, Japanese: , ''Tōkyō'' ), historically known in the west as Tokio and officially the Tokyo Metropolis (, ''Tōkyō-to''), is capital of Japan, the capital and most populous Prefectures of Japan, prefecture of Japan ...

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, making it equivalent to 15.5 bits." In 1979, the first digital pop album,
Bop till You Drop ''Bop Till You Drop'' is Ry Cooder Ryland Peter Cooder (born March 15, 1947) is an American musician, songwriter, film score composer and record producer. He is a multi-instrumentalist but is best known for his slide guitar work, his interest ...
, 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 Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics Electronics compri ...

(CD) brought PCM to consumer audio applications with its introduction in 1982. The CD uses a
44,100 Hz In digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical Sampling (s ...
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 Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usual ...
was enabled by
metal–oxide–semiconductor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), is a type of insulated-gate field-effect transistor The field-effect tran ...
(MOS)
switched capacitorA switched capacitor (SC) is an electronic circuit File:PExdcr01CJC.jpg, 200px, A circuit built on a printed circuit board (PCB). An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, indu ...
(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
CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "see-moss"), also known as complementary-symmetry metal–oxide–semiconductor (COS-MOS), is a type of metal–oxide–semiconductor field-effect transistor The metal–oxide–se ...
(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 In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathema ...
s such as the
public switched telephone network The public switched telephone network (PSTN) provides infrastructure Infrastructure is the set of fundamental facilities and systems that support the sustainable functionality of households and firms. Serving a country, city, or other area, i ...
digitized DigitizationDefinition of digitization
at WhatIs.com
is the process of converting ...
with
very-large-scale integration Very large-scale integration (VLSI) is the process of creating an integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit 200px, A ci ...
(VLSI) CMOS PCM codec-filters, widely used in
electronic switching system In telecommunications, an electronic switching system (ESS) is a telephone switch that uses solid-state electronics, such as digital electronics and computerized common control, to interconnect telephone circuits for the purpose of establishing tele ...
s for
telephone exchanges manually connecting calls with cord pairs at a telephone switchboard A telephone exchange, telephone switch, or central office is a telecommunications Telecommunication is the transmission of information Information can be thought of as ...
, user-end
modems A modulator-demodulator, or simply a modem, is a hardware device that converts data from a digital format, intended for communication directly between devices with specialized wiring, into one suitable for a transmission medium such as telep ...

and a wide range of
digital transmission Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics Electronics comprises the physics, engineering, technology a ...
applications such as the
integrated services digital network Integrated Services Digital Network (ISDN) is a set of communication standards for simultaneous digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics D ...
(ISDN), cordless telephones and
cell phones A mobile phone, cellular phone, cell phone, cellphone, handphone, or hand phone, sometimes shortened to simply mobile, cell or just phone, is a portable telephone that can make and receive telephone call, calls over a radio frequency link wh ...

.

# 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 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 th ...
used also on
Super Audio CD Super Audio CD (SACD) is a read-only optical disc In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithm of an algo ...
.
* 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 (''C ...
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 (also known as AES/EBU) is a technical standard, standard for the exchange of digital audio signals between professional audio devices. An AES3 signal can carry two channels of PCM audio over several transmission medium, transmission media ...
(specified in 1985, upon which
S/PDIF S/PDIF (Sony/Philips Digital Interface) is a type of digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital form. In digital audio, the sound wave of the audio ...
is based) is a particular format using LPCM. * 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 Waveform Audio File Format (WAVE, or WAV due to its filename extension A filename extension, file extension or file type is an identifier specified as a suffix to the name A name is a term used for identification by an external observer. T ...

(defined in 1991) and
AIFF Audio Interchange File Format (AIFF) is an audio file format An audio file format is a file format for storing digital audio data on a computer system. The bit layout of the audio data (excluding metadata) is called the audio coding format and can ...
audio container formats (defined in 1988). LPCM data may also be stored in other formats such as AU,
raw audio format RAW Audio format or just RAW Audio is an audio file format An audio file format is a file format for storing digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital ...
(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 Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital elect ...

(since 1995) and
Blu-ray The Blu-ray Disc (BD), often known simply as Blu-ray, is a digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of elec ...

(since 2006) standards. It is also defined as a part of various digital video and audio storage formats (e.g. since 1995,
AVCHD AVCHD (Advanced Video Coding High Definition) is a file-based format for the digital recording In digital recording, an audio Audio most commonly refers to sound In physics Physics (from grc, φυσική (ἐπιστήμη), phy ...

since 2006). * LPCM is used by
HDMI High-Definition Multimedia Interface (HDMI) is a proprietary hardware, proprietary audio/video Interface (computing), interface for transmitting uncompressed video data and compressed or uncompressed digital audio data from an HDMI-compliant s ...

(defined in 2002), a single-cable digital audio/video connector interface for transmitting uncompressed digital data. *
RF64{{Infobox file format , name = RF64 , icon = , iconcaption = , icon_size = , screenshot = , screenshot_size = , caption = , _noextcode = , extension = , _nomimecode = , mime = , type_code = , uniform_type = , con ...
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 or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of Mechanical equilib ...

(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 An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit 200px, A circuit built on a printed circuit board (PCB). An electronic circuit is composed of indiv ...

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 (signal processing), digit ...
(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 Connection-oriented communication is a network communication mode in telecommunications and computer networking, where a communication session or a semi-permanent connection is established before any useful ...
, generally for transmission of multiple streams over a single physical link. One technique is called
time-division multiplexing Time-division multiplexing (TDM) is a method of transmitting and receiving independent signals over a common signal path by means of synchronized switches at each end of the transmission line so that each signal appears on the line only a fractio ...
(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 , a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a into an . An (ADC) performs the reverse function. There are several DAC ; the suitability of a DAC for a particular application is determined by ...
s (DACs). They produce a
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

or
current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. ...
(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 Reconstruction may refer to: Politics, history, and sociology * Reconstruction (law), the transfer of a company's (or several companies') business to a new company *''Perestroika ''Perestroika'' postage stamp, 1988 Perestroika (; russian: ...
that suppresses energy outside the expected frequency range (greater than the Nyquist frequency $f_s / 2$).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'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 (signal), 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 hertz, kHz as used with
DVD The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital elect ...

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 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 ...
, the usable voice frequency band ranges from approximately 300 Hertz, 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 error swings between -''q''/2 and ''q''/2. In the ideal case (with a fully linear ADC and signal level >> ''q'') it is uniform distribution (continuous), 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); 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, 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 (data), audio compression techniques, such as modified discrete cosine transform (MDCT) coding. * Linear PCM (LPCM) is PCM with linear quantization. * DPCM, 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 (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. * Delta modulation 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. The default signal compression encoding on a DS0 is either Mu-law algorithm, 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 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''.Stallings, William
Digital Signaling Techniques
December 1984, Vol. 22, No. 12, IEEE IEEE Communications Magazine, Communications Magazine
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 pseudorandom, 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. 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 World War II or the Second World War, often abbreviated as WWII or WW2, was a that lasted from 1939 to ...

: filed in 1943: N-ary Pulse Code Modulation.