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"PCM" redirects here. For other uses, see .
Pulse-code modulation (PCM) is a method used to
represent sampled . It is the standard form of
in computers, ,
and other digital audio applications. In a PCM stream, the
of the analog signal is sampled regularly at uniform intervals, and each sample is
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
or the ). 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 , which is the number of times per second th and the , which determines the number of possible digital values that can be used to represent each sample.
Early electrical communications started to sample signals in order to interlace samples from multiple
sources and to convey them over a single telegraph cable. The American inventor
conveyed telegraph
(TDM) as early as 1853. Electrical engineer W. M. Miner, in 1903, used an electro-mechanical
for time-division multiplexing multip he also applied this technology to telephony. He obtained intelligible speech from channels sampled at a rate above  Hz; lower rates proved unsatisfactory. This was TDM, but
(PAM) rather than PCM.
In 1920 the , named after its inventors
and , used telegraph signaling of characters punched in paper tape to send samples of images quantized to 5 whether this is considered PCM or not depends on how one interprets "pulse code", but it involved transmission of quantized samples.
In 1926, Paul M. Rainey of Western Electric patented a
which transmitted its signal using 5-bit PCM, encoded by an opto-mechanical . The machine did not go into production.
British engineer , unaware of previous work, conceived the use of PCM for voice communication in 1937 while working for
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
The first transmission of
by digital techniques, the
encryption equipment, conveyed high-level Allied communications during . In 1943 the
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
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
having encoding perforations. As in an , 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 , and produced all bits simultaneously by using a fan beam instead of a scanning beam.
In the United States, the
has honored
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
in 1945, and issued in 1948: . The three of them published "The Philosophy of PCM" in 1948.
PCM is the method of encoding generally used for uncompressed audio, although there are other methods such as
(used also on ).
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
(informally also known as Audio CD), introduced in 1982.
(specified in 1985, upon which
is based) is a particular format using LPCM.
On PCs, PCM and LPCM often refer to the format used in WAV (defined in 1991) and
audio container formats (defined in 1988). LPCM data may also be stored in other formats such as ,
(header-less file) and various multimedia container formats.
LPCM has been defined as a part of the
(since 1995) and
(since 2006) standards. It is also defined as a part of various digital video and audio storage formats (e.g.
since 1995,
since 2006).
LPCM is used by
(defined in 2002), a single-cable digital audio/video connector interface for transmitting uncompressed digital data.
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.
Sampling and quantization of a signal (red) for 4-bit PCM
In the diagram, a
(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
would result in the following set of : 1000 (23×1+22×0+21×0+20×0=8+0+0+0=8), , , , , etc. These digital values could then be further processed or analyzed by a . Several PCM streams could also be
into a larger aggregate , generally for transmission of multiple streams over a single physical link. One technique is called
(TDM) and is widely used, notably in the modern public telephone system.
The PCM process is commonly implemented on a single
generally referred to as an
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 . 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
{\displaystyle f_{s}/2}
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 , the usable
frequency band ranges from approximately 300  to ;Hz. Therefore, per the , 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
(DACs). They produce a
(depending on type) that represents the value presented on their digital inputs. This output would then generally be filtered and amplified for use.
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
as used with
format videos, or 44.1 kHz as used in . 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 it.
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 .
Between samples no measurement o the
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 ); 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.
In conventional PCM, the
may be processed (e.g., by ) before being digitized. Once the signal is digitized, the PCM signal is usually subjected to further processing (e.g.,
PCM with linear quantization is known as
Some forms of PCM combine signal processing with coding. Older versions of these systems applied the processing in the analog domain as
newer implementations do so in the digital domain. These simple techniques have been largely rendered obsolete by modern transform-based
techniques.
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.
(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 .
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 . The default
encoding on a DS0 is either
PCM (North America and Japan) or
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 . An alternative proposal for a
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 u-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
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
communications.
Main article:
PCM can be either
(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
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
are added into the stream which guarantee at least occasional symbol transitions.
Another technique used to control ones-density is the use of a
which will tend to turn the raw data stream into a stream that looks , 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
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 , where the pulses can be positive, negative or absent. In the typical
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,
and , 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 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 .
– ITU-T standard for audio . It is primarily used in telephony.
(SQNR) – One method of measuring quantization error.
Some systems use
to remove some of the aliasing, converting the signal from digital to analog at a higher sample rate such that the analog
is much simpler. In some systems, no explicit filt 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
over this interval, with zero mean and variance of q2/12.
A slight difference between the encoding and decoding clock frequencies is not gener 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.
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and Bob Badgley invented multi-level PCM independently in their work at Bell Labs on :
filed in 1943: N-ary Pulse Code Modulation.
: A description of PCM with links to information about subtypes of this format (for example ), and references to their specifications.
– Contains links to information about implementations and their specifications.
– Contains information about, and specifications for the implementation of LPCM used in WAV files.
– audio/L8 and audio/L16 (March 2007)
(January 2002)
– L8 and L16 (July 2003)
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