Pulse-code modulation (PCM) is a method used to digitally represent
sampled analog signals. It is the standard form of digital audio in
computers, compact discs, digital telephony and other digital audio
applications. In a PCM stream, the amplitude of the analog signal is
sampled 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 where
the quantization levels are linearly uniform. This is in contrast
to PCM encodings where quantization levels vary as a function of
amplitude (as with the
A-law algorithm or the μ-law algorithm).
Though PCM is a more general term, it is often used to describe data
encoded as LPCM.
A PCM stream has two basic properties that determine the stream's
fidelity to the original analog signal: the sampling rate, which is
the number of times per second that samples are taken; and the bit
depth, which determines the number of possible digital values that can
be used to represent each sample.
5 Standard sampling precision and rates
7 Digitization as part of the PCM process
8 Encoding for serial transmission
10 See also
13 Further reading
14 External links
Early electrical communications started to sample signals in order to
multiplex samples from multiple telegraphy sources and to convey them
over a single telegraph cable. The American inventor Moses G. Farmer
conveyed telegraph time-division multiplexing (TDM) as early as 1853.
Electrical engineer W. M. Miner, in 1903, used an electro-mechanical
commutator for time-division multiplexing multiple telegraph signals;
he also applied this technology to telephony. He obtained intelligible
speech from channels sampled at a rate above 3500–4300 Hz;
lower rates proved unsatisfactory.
In 1920, the
Bartlane cable picture transmission system used telegraph
signaling of characters punched in paper tape to send samples of
images quantized to 5 levels. 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, unaware of previous work, conceived the
use of PCM for voice communication in 1937 while working for
International Telephone and Telegraph
International Telephone and Telegraph in France. He described the
theory and 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 first transmission of speech by digital techniques, the SIGSALY
encryption equipment, conveyed high-level Allied communications during
World War II. In 1943 the
Bell Labs researchers who designed the
SIGSALY system became aware of the use of PCM binary coding as already
proposed by Alec Reeves. In 1949, for the Canadian Navy's DATAR
system, Ferranti Canada built a working PCM radio system that was able
to transmit digitized radar data over long distances.
PCM in the late 1940s and early 1950s used a cathode-ray coding tube
with a plate electrode having encoding perforations. As in an
oscilloscope, the beam was swept horizontally at the sample rate while
the vertical deflection was controlled by the input analog signal,
causing the beam to pass through higher or lower portions of the
perforated plate. The plate collected or passed the beam, producing
current variations in binary code, one bit at a time. Rather than
natural binary, the grid of Goodall's later tube was perforated to
produce a glitch-free Gray code, and produced all bits simultaneously
by using a fan beam instead of a scanning beam.
In the United States, the
National Inventors Hall of Fame
National Inventors Hall of Fame has honored
Bernard M. Oliver and Claude Shannon as the inventors of
PCM, as described in "Communication System Employing Pulse Code
Modulation", U.S. Patent 2,801,281 filed in 1946 and 1952, granted in
1956. Another patent by the same title was filed by
John R. Pierce
John R. Pierce in
1945, and issued in 1948: U.S. Patent 2,437,707. The three of them
published "The Philosophy of PCM" in 1948.
T-carrier system, introduced in 1961, uses two twisted-pair
transmission lines to carry 24 PCM telephone calls sampled at
8 kHz and 8-bit resolution. This development improved capacity
and call quality compared to the previous frequency-division
In 1967, the first PCM recorder was developed by NHK's research
facilities in Japan. The 30 kHz 12-bit device used a
compander (similar to DBX Noise Reduction) to extend the dynamic
range, and stored the signals on a video tape recorder. In 1969, NHK
expanded the system's capabilities to 2-channel stereo and 32 kHz
13-bit resolution. In January 1971, using NHK's PCM recording system,
Denon recorded the first commercial digital
Denon unveiled the first 8-channel digital recorder, the
DN-023R, which used a 4-head open reel broadcast video tape recorder
to record in 47.25 kHz, 13-bit PCM audio.[note 2] In 1977, Denon
developed the portable PCM recording system, the DN-034R. Like the
DN-023R, it recorded 8 channels at 47.25 kHz, but it used 14-bits
"with emphasis, making it equivalent to 15.5 bits."
In 1973, adaptive differential pulse-code modulation (ADPCM) was
developed, by P. Cummiskey, Nikil S. Jayant and James L. Flanagan.
The compact disc (CD) brought PCM to consumer audio applications with
its introduction in 1982. The CD uses a
44,100 Hz sampling frequency
and 16-bit resolution and stores up to 80 minutes of stereo audio per
PCM is the method of encoding generally used for uncompressed audio,
although there are other methods such as pulse-density modulation
(used also on Super Audio CD).
4ESS switch introduced time-division switching into the US
telephone system in 1976, based on medium scale integrated circuit
LPCM is used for the lossless encoding of audio data in the Compact
disc Red Book standard (informally also known as Audio CD), introduced
AES3 (specified in 1985, upon which
S/PDIF is based) is a particular
format using LPCM.
Laserdiscs with digital sound have an LPCM track on the digital
On PCs, PCM and LPCM often refer to the format used in
WAV (defined in
AIFF 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 (since 1995) and Blu-ray
(since 2006) standards. It is also defined as a part of
various digital video and audio storage formats (e.g. DV since
AVCHD since 2006).
LPCM is used by
HDMI (defined in 2002), a single-cable digital
audio/video connector interface for transmitting uncompressed digital
RF64 container format (defined in 2007) uses LPCM and also allows
non-PCM bitstream storage: various compression formats contained in
RF64 file as data bursts (Dolby E, Dolby AC3, DTS, MPEG-1/MPEG-2
Audio) can be "disguised" as PCM linear.
Sampling and quantization of a signal (red) for 4-bit LPCM
In the diagram, a sine wave (red curve) is sampled and quantized for
PCM. The sine wave is sampled at regular intervals, shown as vertical
lines. For each sample, one of the available values (on the y-axis) is
chosen by some algorithm. This produces a fully discrete
representation of the input signal (blue points) 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 8, 9, 11, 13, 14, 15, 15, 15, 14, etc. Encoding
these values as binary numbers would result in the following set of
nibbles: 1000 (23×1+22×0+21×0+20×0=8+0+0+0=8), 1001, 1011, 1101,
1110, 1111, 1111, 1111, 1110, etc. These digital values could then be
further processed or analyzed by a digital signal processor. Several
PCM streams could also be multiplexed into a larger aggregate data
stream, generally for transmission of multiple streams over a single
physical link. One technique is called time-division multiplexing
(TDM) and is widely used, notably in the modern public telephone
The PCM process is commonly implemented on a single integrated circuit
generally referred to as an analog-to-digital converter (ADC).
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 shifts the output
signal to the new value. As a result of these transitions, the signal
has a significant amount of high-frequency energy caused by aliasing.
To remove these undesirable frequencies and leave the original signal,
the demodulator passes the signal through analog filters that suppress
energy outside the expected frequency range (greater than the Nyquist
displaystyle f_ s /2
).[note 3] The sampling theorem shows PCM devices can operate without
introducing distortions within their designed frequency bands if they
provide a sampling frequency twice that of the input signal. For
example, in telephony, the usable voice frequency band ranges from
approximately 300 Hz to 3400 Hz. Therefore, according to the
Nyquist–Shannon sampling theorem, the sampling frequency
(8 kHz) must be at least twice the voice frequency (4 kHz)
for effective reconstruction of the voice signal.
The electronics involved in producing an accurate analog signal from
the discrete data are similar to those used for generating the digital
signal. These devices are Digital-to-analog converters (DACs). They
produce a voltage or current (depending on type) that represents the
value presented on their digital inputs. This output would then
generally be filtered and amplified for use.
Standard sampling precision and rates
Common sample depths for LPCM are 8, 16, 20 or 24 bits per
LPCM encodes a single sound channel. Support for multichannel audio
depends on file format and relies on interweaving or synchronization
of LPCM streams. While two channels (stereo) is the most common
format, some can support up to 8 audio channels (7.1 surround).
Common sampling frequencies are 48 kHz as used with
DVD format videos,
or 44.1 kHz as used in Compact discs. Sampling frequencies of
96 kHz or 192 kHz can be used on some newer equipment, with
the higher value equating to 6.144 megabit per second for two channels
at 16-bit per sample value, but the benefits have been debated.
The bitrate limit for LPCM audio on DVD-Video is also 6.144 Mbit/s,
allowing 8 channels (7.1 surround) × 48 kHz × 16-bit per sample
= 6,144 kbit/s.
There is a L32 bit PCM, and there are many sound cards that support
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.[note 4]
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 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.[note 5]
Digitization as part of the PCM process
In conventional PCM, the analog signal 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 data compression).
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
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.
DPCM (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 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
encoding on a
DS0 is either μ-law (mu-law) PCM (North America and
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. An alternative proposal for a
floating point representation, with 5-bit mantissa and 3-bit exponent,
Where circuit costs are high and loss of voice quality is acceptable,
it sometimes makes sense to compress the voice signal even further. An
DPCM algorithm is used to map a series of 8-bit µ-law or
samples into a series of 4-bit A
DPCM samples. In this way, the
capacity of the line is doubled. The technique is detailed in the
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
DPCM techniques are used in
Voice over IP
Voice over IP communications.
Encoding for serial transmission
Main article: Line code
T-carrier and E-carrier
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 is often controlled using precoding techniques such as
Run Length Limited
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 guarantee at least occasional symbol
Another technique used to control ones-density is the use of a
scrambler polynomial on the raw data 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 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.
The word pulse in the term pulse-code modulation refers to the
"pulses" to be found in the transmission line. This perhaps is a
natural consequence of this technique having evolved alongside two
analog methods, pulse width modulation and pulse position modulation,
in which the information to be encoded is represented by discrete
signal pulses of varying width or position, respectively.[citation
needed] In this respect, PCM bears little resemblance to these other
forms of signal encoding, except that all can be used in time division
multiplexing, and the numbers of the PCM codes are represented as
electrical pulses. The device that performs the coding and decoding
function in a telephone, or other, circuit is called a codec.
Equivalent pulse code modulation noise
Signal-to-quantization-noise ratio (SQNR) – One method of measuring
^ Among the first recordings was Uzu: The World Of Stomu Yamash'ta 2
by Stomu Yamashta.
^ The first recording with this new system was recorded in Tokyo
during April 24–26, 1972.
^ 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.
Quantization error swings between -q/2 and q/2. In the ideal case
(with a fully linear ADC) it is uniformly distributed over this
interval, with zero mean and variance of q2/12.
^ 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,
^ a b c Alvestrand, Harald Tveit; Salsman, James (May 1999). "RFC 2586
– The Audio/L16 MIME content type". The
Internet Society. Retrieved
^ a b c Casner, S. (March 2007). "RFC 4856 – Media Type Registration
of Payload Formats in the RTP Profile for Audio and Video Conferences
– Registration of Media Type audio/L8". The IETF Trust. Retrieved
^ a b c d Bormann, C.; Casner, S.; Kobayashi, K.; Ogawa, A. (January
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and 24-bit Linear Sampled Audio". The
Internet Society. Retrieved
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^ "Claude Shannon". National Inventor's Hall of Fame. Archived from
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quantization in differential PCM coding of speech," Bell Syst. Tech.
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Wikimedia Commons has media related to Pulse-code modulation.
PCM description on MultimediaWiki
Ralph Miller and Bob Badgley invented multi-level PCM independently in
their work at
Bell Labs on SIGSALY: U.S. Patent 3,912,868 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.
Summary of LPCM – Contains links to information about
implementations and their specifications.
How to control internal/external hardware using Microsoft's Media
Control Interface – Contains information about, and specifications
for the implementation of LPCM used in
RFC 4856 – Media Type Registration of Payload Formats in the RTP
Profile for Audio and Video Conferences – audio/L8 and audio/L16
RFC 3190 – RTP Payload Format for 12-bit DAT Audio and 20- and
24-bit Linear Sampled Audio (January 2002)
RFC 3551 – RTP Profile for Audio and Video Conferences with Minimal
Control – L8 and L16 (July 2003)
819 line system
Filming and storage
HD media and
Super Audio CD
Ultra HD Blu-ray
List of digital television deployments by country
Line coding (digital baseband transmission)
Basic line codes
Return to zero (RZ)
Non-return-to-zero, level (NRZ/NRZ-L)
Non-return-to-zero, inverted (NRZ-I)
Non-return-to-zero, space (NRZ-S)
Differential Manchester/biphase (Bi-φ)
Extended line codes
Alternate mark inversion
Modified AMI code
Coded mark inversion
Hybrid ternary code
Optical line codes
See also: Baseband
Ethernet physical layer
Pulse modulation methods
Pulse-amplitude modulation (PAM)
Pulse code modulation
Pulse code modulation (PCM)
Cable protection system
Prepay mobile phone
The Telephone Cases
Timeline of communication technology
Undersea telegraph line
Edwin Howard Armstrong
John Logie Baird
Alexander Graham Bell
Jagadish Chandra Bose
Lee de Forest
Erna Schneider Hoover
Charles K. Kao
Alexander Stepanovich Popov
Johann Philipp Reis
Vladimir K. Zworykin
Free-space optical communication
Network switching (circuit
Public Switched Telephone
World Wide Web