||It has been suggested that Linear pulse-code modulation be merged into this article. (Discuss) Proposed since March 2013.|
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.
PCM streams have two basic properties that determine their fidelity to the original analog signal: the sampling rate, the number of times per second that samples are taken; and the bit depth, 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 multiple telegraphy sources, and convey them over a single telegraph cable. Telegraph time-division multiplexing (TDM) was conveyed as early as 1853, by the American inventor Moses G. Farmer. Electrical engineer W. M. Miner, in 1903, used an electro-mechanical commutator 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; lower rates were unsatisfactory. This was TDM, but pulse-amplitude modulation (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, 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 US patent was granted in 1943.
The first transmission of speech by digital techniques was the SIGSALY encryption equipment used for 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 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 in 1945, and issued in 1948: U.S. Patent 2,437,707. The three of them published "The Philosophy of PCM" in 1948.
PCM was used in Japan by Denon in 1972 for the mastering and production of analogue phonograph records, using a 2-inch Quadruplex-format videotape recorder for its transport, but this was not developed into a consumer product.
In the diagram, a sine wave (red curve) is sampled and quantized for PCM. 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 nibbles: 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. 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 system.
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 frequency ).[note 1] 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, per the Nyquist–Shannon sampling theorem, the sampling frequency (8kHz) must be at least twice the voice frequency (4kHz) 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.
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 2]
- 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 3]
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).
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 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 (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 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. An alternative proposal for a floating point 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 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 communications.
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.
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 guarantee at least occasional symbol transitions.
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 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 circuit is called a codec.
See also 
- Beta encoder
- Equivalent pulse code modulation noise
- G.711 – ITU-T standard for audio companding. It is primarily used in telephony.
- Linear pulse code modulation
- Nyquist–Shannon sampling theorem
- Quantization (signal processing)
- Sampling (signal processing)
- Signal-to-quantization-noise ratio (SQNR) – One method of measuring quantization error.
- Pulse-density modulation
- 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, for example.
- U.S. patent number 1,608,527; also see p. 8, Data conversion handbook, Walter Allan Kester, ed., Newnes, 2005, ISBN 0-7506-7841-0.
- Porter, Arthur. So Many Hills to Climb (2004) Beckham Publications Group
- R. W. Sears, "Electron Beam Deflection Tube for Pulse Code Modulation," Bell Sys. Tech. J., Vol. 27 pp. 44–57
- W. M. Goodall, "Television by Pulse Code Modulation," Bell Sys. Tech. J., Vol. 30 pp. 33–49, 1951.
- "Bernard Oliver". National Inventor's Hall of Fame. Retrieved 6 Feb. 2011.
- "Claude Shannon". National Inventor's Hall of Fame. Retrieved 6 Feb. 2011.
- "National Inventors Hall of Fame announces 2004 class of inventors". Science Blog. February 11, 2004. Retrieved 6 Feb. 2011.
- B. M. Oliver, J. R. Pierce, and C. E. Shannon (Nov. 1948). "The Philosophy of PCM". Proceeding of the IRE 36 (11): 1324–1331. doi:10.1109/JRPROC.1948.231941. ISSN 0096-8390.
- "Linear Pulse Code Modulated Audio (LPCM)". The Library of Congress. Retrieved 2010-03-21.
- Stallings, William, Digital Signaling Techniques, December 1984, Vol. 22, No. 12, IEEE Communications Magazine
Further reading 
- Franklin S. Cooper; Ignatius Mattingly (1969). "Computer-controlled PCM system for investigation of dichotic speech perception". Journal of the Acoustical Society of America 46: 115. doi:10.1121/1.1972688.
- Ken C. Pohlmann (1985). Principles of Digital Audio (2nd ed.). Carmel, Indiana: Sams/Prentice-Hall Computer Publishing. ISBN 0-672-22634-0.
- D. H. Whalen, E. R. Wiley, Philip E. Rubin, and Franklin S. Cooper (1990). "The Haskins Laboratories pulse code modulation (PCM) system". Behavior Research Methods, Instruments, and Computers 22 (6): 550–559. doi:10.3758/BF03204440.
- Bill Waggener (1995). Pulse Code Modulation Techniques (1st ed.). New York, NY: Van Nostrand Reinhold. ISBN 0-442-01436-8.
- Bill Waggener (1999). Pulse Code Modulation Systems Design (1st ed.). Boston, MA: Artech House. ISBN 0-89006-776-7.
- 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.