Pulse-code modulation (PCM) is a digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a numeric (usually binary) code. In Telecommunications, modulation is the process of varying a periodic Waveform, i A digital system uses discrete (discontinuous values usually but not always Symbolized Numerically (hence called "digital" to represent information for In Telecommunication, signalling (UK spelling or signaling (US spelling has the following meanings The use of signals for controlling communications In Signal processing, sampling is the reduction of a Continuous signal to a Discrete signal. In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. PCM has been used in digital telephone systems and 1980s-era electronic musical keyboards. Basic principle A traditional landline telephone system also known as "plain old telephone service" (POTS, commonly handles both signaling and audio information An electronic keyboard or digital keyboard is a type of Keyboard instrument. It is also the standard form for digital audio in computers and the compact disc "red book" format. Digital audio uses Digital signals for Sound reproduction. This includes analog-to-digital conversion, digital-to-analog conversion, storage A computer is a Machine that manipulates data according to a list of instructions. A Compact Disc (also known as a CD) is an Optical disc used to store digital data, originally developed for storing digital audio Red Book is the standard for audio CDs ( Compact Disc Digital Audio system or CDDA) It is also standard in digital video, for example, using ITU-R BT.601. Digital video is a type of Video recording system that works by using a Digital rather than an analog video signal The ITU Radiocommunication Sector ( ITU-R) is one of the three sectors (divisions or units of the International Telecommunication Union (ITU and is responsible for ITU-R Recommendation BT601, more commonly know by the abbreviations Rec However, straight PCM is not typically used for video in standard definition consumer applications such as DVD or DVR because the bit rate required is far too high. DVD (also known as " Digital Versatile Disc " or " Digital Video Disc " - see Etymology)is A digital video recorder ( DVR) or personal video recorder ( PVR) is a device that records video in a digital format to a Disk drive or other Very frequently, PCM encoding facilitates digital transmission from one point to another (within a given system, or geographically) in serial form. In Telecommunication and Computer science, serial communication is the process of sending data one Bit at one time sequentially over a Communication

## Modulation

Sampling and quantization of a signal (red) for 4-bit PCM

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 (in this case, the floor function is used). In Mathematics and Computer science, the floor and ceiling functions map Real numbers to nearby Integers The 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, 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110, etc. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. A nibble (often nybble) is the Computing term for a four- Bit aggregation or half an octet (an octet being an 8-bit Byte These digital values could then be further processed or analyzed by a purpose-specific digital signal processor or general purpose CPU. Digital signal processing ( DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals Several Pulse Code Modulation streams could also be multiplexed into a larger aggregate data stream, generally for transmission of multiple streams over a single physical link. For multiplexing in electronics and signal processing see Multiplexer. This article is about the more general meaning of the term "data stream" This technique is called time-division multiplexing, or TDM, and is widely used, notably in the modern public telephone system. Time-Division Multiplexing ( TDM) is a type of Digital or (rarely analog Multiplexing in which two or more signals or bit streams are transferred

There are many ways to implement a real device that performs this task. In real systems, such a device is commonly implemented on a single integrated circuit that lacks only the clock necessary for sampling, and is generally referred to as an ADC (Analog-to-Digital converter). Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to These devices will produce on their output a binary representation of the input whenever they are triggered by a clock signal, which would then be read by a processor of some sort.

## 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 of the system is shifted instantaneously (in an idealized system) to the new value. As a result of these instantaneous transitions, the discrete signal will have a significant amount of inherent high frequency energy, mostly harmonics of the sampling frequency (see square wave). A square wave is a kind of Non-sinusoidal waveform, most typically encountered in Electronics and Signal processing. To smooth out the signal and remove these undesirable harmonics, the signal would be passed through analog filters that suppress artifacts outside the expected frequency range (i. e. , greater than $\frac{1}{2} f_s$, the maximum resolvable frequency). The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the Sampling frequency Some systems use digital filtering to remove the lowest and largest harmonics. In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling, 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 DACs (digital-to-analog converters), and operate similarly to ADCs. In Electronics, a digital-to-analog converter ( DAC or D-to-A) is a device for converting a digital (usually binary code to an Analog signal They produce on their output a voltage or current (depending on type) that represents the value presented on their inputs. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. This output would then generally be filtered and amplified for use.

## Limitations

There are two sources of impairment implicit in any PCM system:

• Choosing a discrete value near the analog signal for each sample (quantization error)
• Between samples no measurement of the signal is made; due to the sampling theorem this results in any frequency above or equal to $\frac{1}{2} f_s$ (fs being the sampling frequency) being distorted or lost completely (aliasing error). The difference between the actual analog value and quantized digital value due is called quantization error. The Nyquist–Shannon sampling theorem is a fundamental result in the field of Information theory, in particular Telecommunications and Signal processing This article applies to signal processing including computer graphics This is also called the Nyquist frequency. The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the Sampling 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, 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 may be processed (e. An analog or analogue signal is any continuous signal for which the time varying feature (variable of the signal is a representation of some other g. by amplitude compression) before being digitized. Dynamic range compression, also called DRC (often seen in DVD player settings or simply compression, is a process that reduces the Dynamic range of Once the signal is digitized, the PCM signal is usually subjected to further processing (e. g. digital data compression). A digital system uses discrete (discontinuous values usually but not always Symbolized Numerically (hence called "digital" to represent information for

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 A/D process, newer implementations do so in the digital domain. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to These simple techniques have been largely rendered obsolete by modern transform-based audio compression techniques. For processes which reduce the amount of time it takes to listen to and understand a recording see Time-compressed speech.

• Differential (or Delta) pulse-code modulation (DPCM) encodes the PCM values as differences between the current and the previous value. For audio this type of encoding reduces the number of bits required per sample by about 25% compared to PCM. Predict the next sample based on the last few decoded samples.

Minimise mean squared error of prediction residual - use LP coding Good prediction results in a reduction in the dynamic range needed to code the prediction residual and hence a reduction in the bit rate Can use non-uniform quantisation or variable length codes

• 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. Signal-to-noise ratio (often abbreviated SNR or S/N) is an Electrical engineering concept also used in other fields (such as scientific Measurements

Delta modulation, another variant, uses one bit per sample. Delta modulation (DM or Δ-modulation is an analog-to- digital and digital-to- analog signal conversion technique used for transmission of voice information where quality

In telephony, a standard audio signal for a single phone call is encoded as 8000 analog samples per second, of 8 bits each, giving a 64 kbit/s digital signal known as DS0. Digital Signal 0 ( DS0) is a basic Digital signaling rate of 64 Kbit/s, corresponding to the capacity of one Voice-frequency -equivalent 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). In Telecommunication, the term signal compression has the following meanings In analog (usually audio systems reduction of the Dynamic range of a signal An a-law algorithm is a standard Companding algorithm used in European Digital communications systems to optimize i 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. G711 is an ITU-T standard for audio Companding. It is primarily used in Telephony. An alternative proposal for a floating point representation, with 5 bit mantissa and 3 bit radix, was abandoned. In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number.

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. G726 is an ITU-T ADPCM Speech codec standard covering the transmission of voice at rates of 16 24 32 and 40 kbit/s

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. Voice-over-Internet protocol ( VoIP, vɔɪp is a protocol optimized for the transmission of voice through the Internet

## Encoding for transmission

Main article: Line code

Pulse-code modulation can be either return-to-zero (RZ) or non-return-to-zero (NRZ). In Telecommunication, a line code (also called digital baseband modulation) is a Code chosen for use within a Communications system for Return-to-zero (RZ describes a Line code used in Telecommunications signals in which the signal drops (returns to zero between each pulse In Telecommunication, a non-return-to-zero ( NRZ) Line code is a binary code in which "1s" are represented by one Significant 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. Run length limited or RLL coding is a technique that is used to store data on recordable media 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 Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations A pseudorandom process is a process that appears random but is not 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. Direct current ( DC) is the unidirectional flow of Electric charge. 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 Telecommunication, bipolar encoding is a type of Line code (a method of encoding digital information to make it resistant to certain forms of signal loss during In the typical alternate mark inversion code, non-zero pulses alternate between being positive and negative. In Telecommunication, bipolar encoding is a type of Line code (a method of encoding digital information to make it resistant to certain forms of signal loss during These rules may be violated to generate special symbols used for framing or other special purposes.

## History

In the history of electrical communications, the earliest reason for sampling a signal was to interlace samples from different telegraphy sources, and convey them over a single telegraph cable. In Telecommunications T-carrier, sometimes abbreviated as T-CXR, is the generic designator for any of several digitally multiplexed telecommunications Telegraph time-division multiplexing (TDM) was conveyed as early as 1853, by the American inventor M. Time-Division Multiplexing ( TDM) is a type of Digital or (rarely analog Multiplexing in which two or more signals or bit streams are transferred B. Farmer. The 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: below this was unsatisfactory. This was TDM, but pulse-amplitude modulation (PAM) rather than PCM. 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

Paul M. Rainey of Western Electric in 1926 patented a facsimile machine using an optical 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. Alec Harley Reeves, CBE ( March 10, 1902 - October 13, 1971) was a British scientist best known for his invention of ITT Corporation, is a global diversified manufacturing company with 2007 revenues of \$9 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 vocoder encryption equipment used for high-level Allied communications during World War II from 1943. Speech refers to the processes associated with the production and perception of Sounds used in Spoken language. In Cryptography, SIGSALY (also known as the X System, Project X, Ciphony I, and the Green Hornet) was a secure speech A vocoder, ˈvoʊkoʊdər (a Portmanteau of vox/voc ( voice) and encoder) is an analysis / synthesis system mostly used for speech in which the input is World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including 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. Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) is the Research organization 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[1]. DATAR, short for Digital Automated Tracking and Resolving, was a pioneering computerized battlefield information system Ferranti-Packard was the Canadian division of Ferranti 's global manufacturing empire formed by the 1958 merger of Ferranti Electric and Packard Electric

PCM in the 1950s used a cathode-ray coding tube with a grid 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 grid. An oscilloscope (commonly abbreviated to scope or O-scope) is a type of Electronic test equipment that allows signal Voltages to be viewed The grid interrupted the beam, producing current variations in binary code. Rather than natural binary, the grid was perforated to produce Gray code lest a sweep along a transition zone produce glitches. Name Bell Labs researcher Frank Gray introduced the term reflected binary code in his 1947 patent application remarking that the code had "as

## 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. Pulse-width modulation (PWM of a signal or power source involves the Modulation of its Duty cycle, to either convey information over a Pulse-position modulation is a form of signal Modulation in which M message bits are encoded by transmitting asingle pulse in one of 2^M possible time-shifts 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. A codec is a device or program capable of encoding and/or decoding a Digital Data stream or signal.

• Compact disc – The Red Book audio CD consists of several stereo tracks stored using 16-bit PCM coding. A Compact Disc (also known as a CD) is an Optical disc used to store digital data, originally developed for storing digital audio Red Book is the standard for audio CDs ( Compact Disc Digital Audio system or CDDA)
• Equivalent pulse code modulation noise
• G.711 – ITU-T standard for audio companding. In Telecommunication, equivalent pulse code modulation noise (PCM is the amount of Thermal noise power on a Frequency-division multiplexing G711 is an ITU-T standard for audio Companding. It is primarily used in Telephony. It is primarily used in telephony.
• Linear Pulse Code Modulation
• Nyquist–Shannon sampling theorem
• Pulse-width modulation
• Quantization (signal processing)
• Sampling (signal processing)
• SQNR – One method of measuring quantization error. Linear pulse code modulation ( LPCM) is a method of encoding audio information digitally The Nyquist–Shannon sampling theorem is a fundamental result in the field of Information theory, in particular Telecommunications and Signal processing Pulse-width modulation (PWM of a signal or power source involves the Modulation of its Duty cycle, to either convey information over a In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small In Signal processing, sampling is the reduction of a Continuous signal to a Discrete signal. The acronym SQNR (standing for Signal-to-Quantization Noise Ratio) is widely used in communication systems analysis particularly in PCM ( pulse code modulation) schemes

## References

1. ^ Porter, Arthur. So Many Hills to Climb (2004) Beckham Publications Group
• Franklin S. Cooper; Ignatius Mattingly (1969). Franklin Seaney Cooper (Apr 29 1908 - Feb 20 1999 was an American Physicist and inventor who was a pioneer in speech research "Computer-controlled PCM system for investigation of dichotic speech perception". Journal of the Acoustical Society of America 46: 115.
• 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. Douglas H Whalen is an American linguist who is presently a program officer at the National Science Foundation where he is affiliated with the Cognitive Neuroscience[http R. Wiley, Philip E. Rubin, and Franklin S. Cooper (1990). Philip E Rubin (born May 22 1949, in Newark, New Jersey) is an American cognitive scientist who since 2003 has been the Chief Executive Franklin Seaney Cooper (Apr 29 1908 - Feb 20 1999 was an American Physicist and inventor who was a pioneer in speech research "The Haskins Laboratories pulse code modulation (PCM) system". Haskins Laboratories is an independent international multidisciplinary community of researchers conducting basic Research on spoken and written Behavior Research Methods, Instruments, and Computers 22: 550-559.
• Bill Waggener (1995). Pulse Code Modulation Techniques, 1st ed. , New York, NY: Van Nostrand Reinhold. ISBN 0-442-01436-8.
• William N. Waggener (1999). Pulse Code Modulation Systems Design, 1st ed. , Boston, MA: Artech House. ISBN 0-89006-776-7.