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Pulse-code modulation

Pulse-code modulation

Overview
Pulse-code modulation is a method used to digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

ly represent sampled analog signal
Analog signal
An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

s. It is the standard form for digital audio
Digital audio
Digital audio is sound reproduction using pulse-code modulation and digital signals. Digital audio systems include analog-to-digital conversion , digital-to-analog conversion , digital storage, processing and transmission components...

 in computers and various Blu-ray, Compact Disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

 and DVD
DVD
A DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....

 formats, as well as other uses such as digital telephone
Telephone
The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 systems. A PCM stream is a digital representation of an analog signal, in which the magnitude of the analogue signal is sampled regularly at uniform intervals, with each sample being quantized
Quantization (signal processing)
Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

 to the nearest value within a range of digital steps.

PCM streams have two basic properties that determine their fidelity to the original analog signal: the sampling rate
Sampling rate
The sampling rate, sample rate, or sampling frequency defines the number of samples per unit of time taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz , sometimes noted as Sa/s...

, which is the number of times per second that samples are taken; and the bit depth
Audio bit depth
In digital audio, bit depth describes the number of bits of information recorded for each sample. Bit depth directly corresponds to the resolution of each sample in a set of digital audio data...

, which determines the number of possible digital values that each sample can take.

In the history of electrical communications, the earliest reason for sampling a signal was to interlace samples from different telegraphy
Telegraphy
Telegraphy is the long-distance transmission of messages via some form of signalling technology. Telegraphy requires messages to be converted to a code which is known to both sender and receiver...

 sources, and convey them over a single telegraph cable.
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Encyclopedia
Pulse-code modulation is a method used to digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

ly represent sampled analog signal
Analog signal
An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

s. It is the standard form for digital audio
Digital audio
Digital audio is sound reproduction using pulse-code modulation and digital signals. Digital audio systems include analog-to-digital conversion , digital-to-analog conversion , digital storage, processing and transmission components...

 in computers and various Blu-ray, Compact Disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

 and DVD
DVD
A DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....

 formats, as well as other uses such as digital telephone
Telephone
The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 systems. A PCM stream is a digital representation of an analog signal, in which the magnitude of the analogue signal is sampled regularly at uniform intervals, with each sample being quantized
Quantization (signal processing)
Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

 to the nearest value within a range of digital steps.

PCM streams have two basic properties that determine their fidelity to the original analog signal: the sampling rate
Sampling rate
The sampling rate, sample rate, or sampling frequency defines the number of samples per unit of time taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz , sometimes noted as Sa/s...

, which is the number of times per second that samples are taken; and the bit depth
Audio bit depth
In digital audio, bit depth describes the number of bits of information recorded for each sample. Bit depth directly corresponds to the resolution of each sample in a set of digital audio data...

, which determines the number of possible digital values that each sample can take.

History


In the history of electrical communications, the earliest reason for sampling a signal was to interlace samples from different telegraphy
Telegraphy
Telegraphy is the long-distance transmission of messages via some form of signalling technology. Telegraphy requires messages to be converted to a code which is known to both sender and receiver...

 sources, and convey them over a single telegraph cable. Telegraph time-division multiplexing
Time-division multiplexing
Time-division multiplexing is a type of digital multiplexing in which two or more bit streams or signals are transferred apparently simultaneously as sub-channels in one communication channel, but are physically taking turns on the channel. The time domain is divided into several recurrent...

 (TDM) was conveyed as early as 1853, by the American inventor Moses G. Farmer
Moses G. Farmer
Moses Gerrish Farmer was an electrical engineer and inventor. Farmer was a member to the AIEE, later known as the IEEE.-Biography:...

. The electrical engineer W. M. Miner, in 1903, used an electro-mechanical commutator
Commutator (electric)
A commutator is a rotary electrical switch in certain types of electric motors or electrical generators that periodically reverses the current direction between the rotor and the external circuit. In a motor, it applies power to the best location on the rotor, and in a generator, picks off power...

 for time-division multiplex of multiple telegraph signals, and also applied this technology to telephony. He obtained intelligible speech from channels sampled at a rate above 3500–4300 Hz: below this was unsatisfactory. This was TDM, but pulse-amplitude modulation
Pulse-amplitude modulation
Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses....

 (PAM) rather than PCM.

In 1926, Paul M. Rainey of Western Electric patented a facsimile machine which transmitted its signal using 5-bit PCM, encoded by an opto-mechanical analog-to-digital converter. The machine did not go into production. British engineer Alec Reeves
Alec Reeves
Alec Harley Reeves, CBE was a British scientist best known for his invention of pulse-code modulation . He was awarded 82 patents.-Early life:...

, 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 advantages, but no practical use resulted. Reeves filed for a French patent in 1938, and his U.S. patent was granted in 1943.

The first transmission of speech by digital techniques was the SIGSALY
SIGSALY
In cryptography, SIGSALY was a secure speech system used in World War II for the highest-level Allied communications....

 encryption equipment used for high-level Allied communications during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

. In 1943, the Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

 researchers who designed the SIGSALY system became aware of the use of PCM binary coding as already proposed by Alec Reeves. In 1949 for the Canadian Navy's DATAR
DATAR
DATAR, short for Digital Automated Tracking and Resolving, was a pioneering computerized battlefield information system.Development on DATAR was started by the Canadian Navy in partnership with Ferranti Canada in 1949. DATAR combined data from various ships providing commanders with an "overall...

 system, Ferranti
Ferranti-Packard
Ferranti-Packard Ltd. was the Canadian division of Ferranti's global manufacturing empire, formed by the 1958 merger of Ferranti Electric and Packard Electric...

 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
Plate electrode
A plate is a type of electrode that formed part of a vacuum tube. The plate is impressed with a positive charge so that it may capture and flow electrons within a circuit....

 having encoding perforations. As in an oscilloscope
Oscilloscope
An oscilloscope is a type of electronic test instrument that allows observation of constantly varying signal voltages, usually as a two-dimensional graph of one or more electrical potential differences using the vertical or 'Y' axis, plotted as a function of time,...

, 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
Gray code
The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit. It is a non-weighted code....

, and produced all bits simultaneously by using a fan beam instead of a scanning beam.

The National Inventors Hall of Fame
National Inventors Hall of Fame
The National Inventors Hall of Fame is a not-for-profit organization dedicated to recognizing, honoring and encouraging invention and creativity through the administration of its programs. The Hall of Fame honors the men and women responsible for the great technological advances that make human,...

 has honored Bernard M. Oliver
Bernard M. Oliver
Bernard M. Oliver , aka Barney Oliver, was a scientist who made contributions in many fields, including radar, television, and computers. He was the founder and director of Hewlett Packard laboratories until his retirement in 1981. He is also a recognized pioneer in the search for...


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.

Pulse-code modulation (PCM) was used in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

 by Denon
Denon
is a Japanese electronics company that was involved in the early stages of development of digital audio technology, while specializing in the manufacture of high-fidelity professional and consumer audio equipment. For many decades, Denon was a brand name of Nippon-Columbia, including the Nippon...

 in 1972 for the mastering and production of analogue phonograph records, using a 2-inch Quadruplex-format videotape recorder for its transport
Transport (recording)
A transport is a device that handles a particular physical storage medium itself, and extracts or records the information to and from the medium, to an outboard set of processing electronics that the transport is connected to.A transport houses no electronics itself for encoding and decoding the...

, but this was not developed into a consumer product
Consumer product
A consumer product is generally any tangible personal property for sale and that is used for personal, family, or household for non-business purposes. The determination whether a good is a consumer product requires a factual finding, on a case-by-case basis...

.

Modulation


In the diagram, a sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

 (red curve) is sampled and quantized for pulse code modulation. The sine wave is sampled at regular intervals, shown as ticks on the x-axis. For each sample, one of the available values (ticks on the y-axis) is chosen by some algorithm. This produces a fully discrete representation of the input signal (shaded area) that can be easily encoded as digital data for storage or manipulation. For the sine wave example at right, we can verify that the quantized values at the sampling moments are 7, 9, 11, 12, 13, 14, 14, 15, 15, 15, 14, etc. Encoding these values as binary numbers would result in the following set of nibble
Nibble
In computing, a nibble is a four-bit aggregation, or half an octet...

s: 0111 (23×0+22×1+21×1+20×1=0+4+2+1=7), 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110, etc. These digital values could then be further processed or analyzed by a digital signal processor
Digital signal processor
A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...

. Several PCM streams could also be multiplexed
Multiplexing
The multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...

 into a larger aggregate data stream
Data stream
In telecommunications and computing, a data stream is a sequence of digitally encoded coherent signals used to transmit or receive information that is in the process of being transmitted....

, generally for transmission of multiple streams over a single physical link. One technique is called time-division multiplexing
Time-division multiplexing
Time-division multiplexing is a type of digital multiplexing in which two or more bit streams or signals are transferred apparently simultaneously as sub-channels in one communication channel, but are physically taking turns on the channel. The time domain is divided into several recurrent...

 (TDM) and is widely used, notably in the modern public telephone system.

The PCM process is commonly implemented on a single integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

 and is generally referred to as an analog-to-digital converter
Analog-to-digital converter
An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

 (ADC).

Demodulation


To produce output from the sampled data, the procedure of modulation is applied in reverse. After each sampling period has passed, the next value is read and the output signal is shifted to the new value. As a result of these transitions, the signal will have a significant amount of high-frequency energy. To smooth out the signal and remove these undesirable aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

 frequencies, the signal is passed through analog filters that suppress energy outside the expected frequency range (that is, greater than the Nyquist frequency
Nyquist frequency
The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...

 ).Some systems use digital filter
Digital filter
In electronics, computer science and mathematics, 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 filter, the analog filter, which is...

ing to remove some of the aliasing, converting the signal from digital to analog at a higher sample rate such that the analog filter required for anti-aliasing
Anti-aliasing
In digital signal processing, spatial anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution...

 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.
The sampling theorem suggests that practical PCM devices, provided a sampling frequency that is sufficiently greater than that of the input signal, can operate without introducing significant distortions within their designed frequency bands.

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
Digital-to-analog converter
In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...

s (DACs), and operate similarly to ADCs. They produce on their output a voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 or current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 (depending on type) that represents the value presented on their digital inputs. This output would then generally be filtered and amplified for use.

Limitations


There are potential sources of impairment implicit in any PCM system:
  • Choosing a discrete value near the analog signal for each sample leads to quantization error
    Quantization error
    In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation...

    .Quantization error swings between -q/2 and q/2. In the ideal case (with a fully linear ADC) it is uniformly distributed
    Uniform distribution (continuous)
    In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by...

     over this interval, with zero mean and variance of q2/12.
  • 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
    Nyquist frequency
    The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...

    ); higher frequencies will generally not be correctly represented or recovered.
  • As samples are dependent on time, an accurate clock is required for accurate reproduction. If either the encoding or decoding clock is not stable, its frequency drift 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 is not stable, however. A drifting clock, even with a relatively small error, will cause very obvious distortions in audio and video signals, for example.

Digitization as part of the PCM process


In conventional PCM, the analog signal
Analog signal
An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

 may be processed (e.g., by amplitude compression) before being digitized. Once the signal is digitized, the PCM signal is usually subjected to further processing (e.g., digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

 data compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....

).

PCM with linear quantization is known as Linear PCM (LPCM).

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.
  • DPCM
    DPCM
    Differential pulse-code modulation is a signal encoder that uses the baseline of pulse-code modulation but adds some functionalities based on the prediction of the samples of the signal...

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

     (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
    Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...

    .
  • Delta modulation
    Delta modulation
    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 where the difference between successive samples is encoded...

     is a form of DPCM which uses one bit per sample.


In telephony, a standard audio signal for a single phone call is encoded as 8,000 analog samples per second, of 8 bits each, giving a 64 kbit/s digital signal known as DS0. The default signal compression
Signal compression
In telecommunication, the term signal compression has the following meanings:In analog systems, reduction of the dynamic range of a signal by controlling it as a function of the inverse relationship of its instantaneous value relative to a specified reference level.Signal compression is usually...

 encoding on a DS0 is either μ-law (mu-law)
Mu-law algorithm
The µ-law algorithm is a companding algorithm, primarily used in the digital telecommunication systems of North America and Japan. Companding algorithms reduce the dynamic range of an audio signal...

 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
G.711
G.711 is an ITU-T standard for audio companding. It is primarily used in telephony. The standard was released for usage in 1972. Its formal name is Pulse code modulation of voice frequencies. It is required standard in many technologies, for example in H.320 and H.323 specifications. It can also...

. An alternative proposal for a floating point
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...

 representation, with 5-bit mantissa and 3-bit radix, was abandoned.

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
G.726
G.726 is an ITU-T ADPCM speech codec standard covering the transmission of voice at rates of 16, 24, 32, and 40 kbit/s. It was introduced to supersede both G.721, which covered ADPCM at 32 kbit/s, and G.723, which described ADPCM for 24 and 40 kbit/s. G.726 also introduced a new...

 standard.

Later it was found that even further compression was possible and additional standards were published. Some of these international standards describe systems and ideas which are covered by privately owned patents and thus use of these standards requires payments to the patent holders.

Some ADPCM techniques are used in Voice over IP
Voice over IP
Voice over Internet Protocol is a family of technologies, methodologies, communication protocols, and transmission techniques for the delivery of voice communications and multimedia sessions over Internet Protocol networks, such as the Internet...

 communications.

Encoding for serial transmission


Pulse-code modulation can be either return-to-zero
Return-to-zero
For the Delp/Goudreau band, see RTZReturn-to-zero describes a line code used in telecommunications signals in which the signal drops to zero between each pulse. This takes place even if a number of consecutive 0's or 1's occur in the signal. The signal is self-clocking...

 (RZ) or non-return-to-zero
Non-return-to-zero
In telecommunication, a non-return-to-zero line code is a binary code in which 1's are represented by one significant condition and 0's are represented by some other significant condition , with no other neutral or rest condition. The pulses have more energy than a RZ code...

 (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.

Ones-density is often controlled using precoding techniques such as Run Length Limited
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. This is used in both telecommunication and storage systems which move a medium past a fixed head. Specifically, RLL bounds the length of stretches ...

 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 guarantee at least occasional symbol transitions.

Another technique used to control ones-density is the use of a scrambler polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

 on the raw data
Raw data
'\putang inaIn computing, it may have the following attributes: possibly containing errors, not validated; in sfferent formats; uncoded or unformatted; and suspect, requiring confirmation or citation. For example, a data input sheet might contain dates as raw data in many forms: "31st January...

 which will tend to turn the raw data stream into a stream that looks pseudo-random, but where the raw stream can be recovered exactly by reversing the effect of the polynomial. In this case, long runs of zeroes or ones are still possible on the output, but are considered unlikely enough to be within normal engineering tolerance.

In other cases, the long term DC
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...

 value of the modulated signal is important, as building up a DC offset will tend to bias detector circuits out of their operating range. In this case special measures are taken to keep a count of the cumulative DC offset, and to modify the codes if necessary to make the DC offset 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 in fact 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 binary numbers of the PCM codes are represented as electrical pulses. The device that performs the coding and decoding function in a telephone circuit is called a codec
Codec
A codec is a device or computer program capable of encoding or decoding a digital data stream or signal. The word codec is a portmanteau of "compressor-decompressor" or, more commonly, "coder-decoder"...

.

See also

  • Beta encoder
    Beta encoder
    A beta encoder is an analog to digital conversion system in which a real number in the unit interval is represented by a finite representation of a sequence in base beta, with beta being a real number between 1 and 2...

  • Equivalent pulse code modulation noise
    Equivalent pulse code modulation noise
    In telecommunication, equivalent pulse code modulation noise is the amount of thermal noise power on a frequency-division multiplexing or wire channel necessary to approximate the same judgment of speech quality created by quantizing noise in a PCM channel....

  • G.711
    G.711
    G.711 is an ITU-T standard for audio companding. It is primarily used in telephony. The standard was released for usage in 1972. Its formal name is Pulse code modulation of voice frequencies. It is required standard in many technologies, for example in H.320 and H.323 specifications. It can also...

     – ITU-T standard for audio companding
    Companding
    In telecommunication, signal processing, and thermodynamics, companding is a method of mitigating the detrimental effects of a channel with limited dynamic range...

    . It is primarily used in telephony.
  • Linear pulse code modulation
  • Nyquist–Shannon sampling theorem
    Nyquist–Shannon sampling theorem
    The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...

  • Pulse-width modulation
    Pulse-width modulation
    Pulse-width modulation , or pulse-duration modulation , is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches....

  • Quantization (signal processing)
    Quantization (signal processing)
    Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

  • Sampling (signal processing)
    Sampling (signal processing)
    In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....

  • Signal-to-quantization-noise ratio (SQNR) – One method of measuring quantization error.
  • Pulse-density modulation
    Pulse-density modulation
    Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with digital data. In a PDM signal, specific amplitude values are not encoded into pulses of different size as they would be in PCM. Instead, it is the relative density of the pulses that corresponds to...


External links

  • PCM description on MultimediaWiki
  • Ralph Miller and Bob Badgley invented multi-level PCM independently in their work at Bell Labs on SIGSALY
    SIGSALY
    In cryptography, SIGSALY was a secure speech system used in World War II for the highest-level Allied communications....

    : filed in 1943: N-ary Pulse Code Modulation.
  • Information about PCM: A description of PCM with links to information about subtypes of this format (for example Linear Pulse Code Modulation), and references to their specifications.