76-543: Pulse-code modulation ( PCM ) is a method used to digitally represent 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 at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Alec Reeves , Claude Shannon , Barney Oliver and John R. Pierce are credited with its invention. Linear pulse-code modulation ( LPCM )
152-401: A 0 bit leaves the order of the code words unchanged, prepending a 1 bit reverses the order of the code words. If the bits at position i {\displaystyle i} of codewords are inverted, the order of neighbouring blocks of 2 i {\displaystyle 2^{i}} codewords is reversed. For example, if bit 0 is inverted in a 3 bit codeword sequence,
228-422: A digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause
304-469: A digital signal is a discrete time , quantized amplitude signal . In other words, it is a sampled signal consisting of samples that take on values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers ). If that discrete set is finite, the discrete values can be represented with digital words of a finite width . Most commonly, these discrete values are represented as fixed-point words (either proportional to
380-518: A hypercube , where each bit is seen as one dimension. When the French engineer Émile Baudot changed from using a 6-unit (6-bit) code to 5-unit code for his printing telegraph system, in 1875 or 1876, he ordered the alphabetic characters on his print wheel using a reflected binary code, and assigned the codes using only three of the bits to vowels. With vowels and consonants sorted in their alphabetical order, and other symbols appropriately placed,
456-416: 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. 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 transitions the output signal to the new value. As
532-410: 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 . Where circuit costs are high and loss of voice quality is acceptable, it sometimes makes sense to compress
608-523: A Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation operation in the prefix sum is performed modulo two. To construct the binary-reflected Gray code iteratively, at step 0 start with the c o d e 0 = 0 {\displaystyle \mathrm {code} _{0}={\mathtt {0}}} , and at step i > 0 {\displaystyle i>0} find
684-481: 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
760-440: A binary value into the corresponding Gray code. Each bit is inverted if the next higher bit of the input value is set to one. This can be performed in parallel by a bit-shift and exclusive-or operation if they are available: the n th Gray code is obtained by computing n ⊕ ⌊ n 2 ⌋ {\displaystyle n\oplus \left\lfloor {\tfrac {n}{2}}\right\rfloor } . Prepending
836-401: A binary-reflected Gray code (BRGC). However, mathematicians have discovered other kinds of Gray codes. Like BRGCs, each consists of a list of words, where each word differs from the next in only one digit (each word has a Hamming distance of 1 from the next word). It is possible to construct binary Gray codes with n bits with a length of less than 2 , if the length is even. One possibility
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#1732856122193912-468: A constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise . Digital logic designers use Gray codes extensively for passing multi-bit count information between synchronous logic that operates at different clock frequencies. The logic is considered operating in different "clock domains". It is fundamental to the design of large chips that operate with many different clocking frequencies. If
988-415: A dual-port FIFO are often stored using Gray code to prevent invalid transient states from being captured when the count crosses clock domains. The updated read and write pointers need to be passed between clock domains when they change, to be able to track FIFO empty and full status in each domain. Each bit of the pointers is sampled non-deterministically for this clock domain transfer. So for each bit, either
1064-455: 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. 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
1140-407: A pattern of 4 on, 4 off; the i -th least significant bit a pattern of 2 on 2 off. The most significant digit is an exception to this: for an n -bit Gray code, the most significant digit follows the pattern 2 on, 2 off, which is the same (cyclic) sequence of values as for the second-most significant digit, but shifted forwards 2 places. The four-bit version of this is shown below: For decimal 15
1216-581: 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 that 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
1292-542: A result of these transitions, the signal retains a significant amount of high-frequency energy due to imaging effects. To remove these undesirable frequencies, the demodulator passes the signal through a reconstruction filter that suppresses energy outside the expected frequency range (greater than the Nyquist frequency f s / 2 {\displaystyle f_{s}/2} ). Common sample depths for LPCM are 8, 16, 20 or 24 bits per sample . LPCM encodes
1368-498: A single sound channel. Support for multichannel audio depends on file format and relies on synchronization of multiple LPCM streams. While two channels (stereo) is the most common format, systems can support up to 8 audio channels (7.1 surround) or more. Common sampling frequencies are 48 kHz as used with DVD format videos, or 44.1 kHz as used in CDs. Sampling frequencies of 96 kHz or 192 kHz can be used on some equipment, but
1444-581: A solution guide for the Towers of Hanoi problem, based on a game by the French Édouard Lucas in 1883. Similarly, the so-called Towers of Bucharest and Towers of Klagenfurt game configurations yield ternary and pentary Gray codes. Martin Gardner wrote a popular account of the Gray code in his August 1972 Mathematical Games column in Scientific American . The code also forms a Hamiltonian cycle on
1520-541: A system has to cycle sequentially through all possible combinations of on-off states of some set of controls, and the changes of the controls require non-trivial expense (e.g. time, wear, human work), a Gray code minimizes the number of setting changes to just one change for each combination of states. An example would be testing a piping system for all combinations of settings of its manually operated valves. A balanced Gray code can be constructed, that flips every bit equally often. Since bit-flips are evenly distributed, this
1596-470: A time, faster algorithms exist. On newer processors, the number of ALU instructions in the decoding step can be reduced by taking advantage of the CLMUL instruction set . If MASK is the constant binary string of ones ended with a single zero digit, then carryless multiplication of MASK with the grey encoding of x will always give either x or its bitwise negation. In practice, "Gray code" almost always refers to
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#17328561221931672-424: A time, for example the output of an event counter which is being passed between clock domains or to a digital-to-analog converter. The advantage of Gray codes in these applications is that differences in the propagation delays of the many wires that represent the bits of the code cannot cause the received value to go through states that are out of the Gray code sequence. This is similar to the advantage of Gray codes in
1748-428: A time, so there is never any ambiguity of position, resulting in codes assigning to each of a contiguous set of integers , or to each member of a circular list, a word of symbols such that no two code words are identical and each two adjacent code words differ by exactly one symbol. These codes are also known as unit-distance , single-distance , single-step , monostrophic or syncopic codes , in reference to
1824-625: 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
1900-405: Is G 1 = ( 0,1 ). This can be thought of as built recursively as above from a zero-bit Gray code G 0 = ( Λ ) consisting of a single entry of zero length. This iterative process of generating G n +1 from G n makes the following properties of the standard reflecting code clear: These characteristics suggest a simple and fast method of translating
1976-451: Is a specific type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which 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
2052-906: Is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be " 001 " and "2" would be " 010 ". In Gray code, these values are represented as " 001 " and " 011 ". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. The use of Gray code in these devices helps simplify logic operations and reduce errors in practice. Many devices indicate position by closing and opening switches. If that device uses natural binary codes , positions 3 and 4 are next to each other but all three bits of
2128-434: Is impossible to make all bits change at exactly the same time. If, at the moment the position is sampled, some bits have changed and others have not, the sampled position will be incorrect. In the case of absolute encoders, the indicated position may be far away from the actual position and, in the case of incremental encoders, this can corrupt position tracking. In contrast, the Gray code used by position encoders ensures that
2204-421: Is optimal in the following way: balanced Gray codes minimize the maximal count of bit-flips for each digit. George R. Stibitz utilized a reflected binary code in a binary pulse counting device in 1941 already. A typical use of Gray code counters is building a FIFO (first-in, first-out) data buffer that has read and write ports that exist in different clock domains. The input and output counters inside such
2280-461: Is sometimes misattributed to 19th century electrical device inventor Elisha Gray . Reflected binary codes were applied to mathematical puzzles before they became known to engineers. The binary-reflected Gray code represents the underlying scheme of the classical Chinese rings puzzle , a sequential mechanical puzzle mechanism described by the French Louis Gros in 1872. It can serve as
2356-461: The Hamming distance of 1 between adjacent codes. In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code , or BRGC . Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943. Frank Gray introduced
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2432-554: The Nyquist limit and does not saturate the quantizer. Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 24-bit (16.8 million levels), and 32-bit (4.3 billion levels) using pulse-code modulation where the number of quantization levels is not necessarily limited to powers of two . A floating point representation is used in many DSP applications. Gray code The reflected binary code ( RBC ), also known as reflected binary ( RB ) or Gray code after Frank Gray ,
2508-629: 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 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
2584-472: The public switched telephone network (PSTN) had been largely digitized with very-large-scale integration (VLSI) CMOS PCM codec-filters, widely used in electronic switching systems for telephone exchanges , user-end modems and a wide range of digital transmission applications such as the integrated services digital network (ISDN), cordless telephones and cell phones . PCM is the method of encoding typically used for uncompressed digital audio. In
2660-536: The 5-bit character code has been recognized as a reflected binary code. This code became known as Baudot code and, with minor changes, was eventually adopted as International Telegraph Alphabet No. 1 (ITA1, CCITT-1) in 1932. About the same time, the German-Austrian Otto Schäffler [ de ] demonstrated another printing telegraph in Vienna using a 5-bit reflected binary code for
2736-437: The benefits have been debated. The Nyquist–Shannon sampling theorem shows PCM devices can operate without introducing distortions within their designed frequency bands if they provide a sampling frequency at least twice that of the highest frequency contained in the input signal. For example, in telephony , the usable voice frequency band ranges from approximately 300 Hz to 3400 Hz. For effective reconstruction of
2812-462: The binary data bits into the binary-to-Gray conversion circuit will mean that the code could go briefly through states that are wildly out of sequence. Adding a clocked register after the circuit that converts the count value to Gray code may introduce a clock cycle of latency, so counting directly in Gray code may be advantageous. To produce the next count value in a Gray-code counter, it is necessary to have some combinational logic that will increment
2888-402: The binary representation differ: The problem with natural binary codes is that physical switches are not ideal: it is very unlikely that physical switches will change states exactly in synchrony. In the transition between the two states shown above, all three switches change state. In the brief period while all are changing, the switches will read some spurious position. Even without keybounce ,
2964-450: The bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise . Despite the fact that Stibitz described this code before Gray,
3040-724: The bit position of the least significant 1 in the binary representation of i {\displaystyle i} and flip the bit at that position in the previous code c o d e i − 1 {\displaystyle \mathrm {code} _{i-1}} to get the next code c o d e i {\displaystyle \mathrm {code} _{i}} . The bit positions start 0, 1, 0, 2, 0, 1, 0, 3, .... See find first set for efficient algorithms to compute these values. The following functions in C convert between binary numbers and their associated Gray codes. While it may seem that Gray-to-binary conversion requires each bit to be handled one at
3116-445: The channel. In other cases, extra framing bits are added into the stream, which guarantees at least occasional symbol transitions. Another technique used to control ones-density is the use of a scrambler on the data, which will tend to turn the data stream into a stream that looks pseudo-random , but where the data can be recovered exactly by a complementary descrambler. In this case, long runs of zeroes or ones are still possible on
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3192-532: The code allow for mostly incremental changes, but occasionally a single bit-change can cause a big leap and lead to new properties. Gray codes are also used in labelling the axes of Karnaugh maps since 1953 as well as in Händler circle graphs since 1958, both graphical methods for logic circuit minimization . In modern digital communications , 1D- and 2D-Gray codes play an important role in error prevention before applying an error correction . For example, in
3268-407: The code rolls over to decimal 0 with only one switch change. This is called the cyclic or adjacency property of the code. In modern digital communications , Gray codes play an important role in error correction . For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that
3344-399: The codes for any two consecutive positions will differ by only one bit and, consequently, only one bit can change at a time. In this case, the maximum position error will be small, indicating a position adjacent to the actual position. Due to the Hamming distance properties of Gray codes, they are sometimes used in genetic algorithms . They are very useful in this field, since mutations in
3420-408: The construction of mechanical encoders, however the source of the Gray code is an electronic counter in this case. The counter itself must count in Gray code, or if the counter runs in binary then the output value from the counter must be reclocked after it has been converted to Gray code, because when a value is converted from binary to Gray code, it is possible that differences in the arrival times of
3496-419: The current count value that is stored. One way to increment a Gray code number is to convert it into ordinary binary code, add one to it with a standard binary adder, and then convert the result back to Gray code. Other methods of counting in Gray code are discussed in a report by Robert W. Doran , including taking the output from the first latches of the master-slave flip flops in a binary ripple counter. As
3572-539: 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. The PCM process is commonly implemented on a single integrated circuit called an analog-to-digital converter (ADC). This produces a fully discrete representation of the input signal (blue points) that can be easily encoded as digital data for storage or manipulation. Several PCM streams could also be multiplexed into
3648-419: The digital domain. These simple techniques have been largely rendered obsolete by modern transform-based audio compression techniques, such as modified discrete cosine transform (MDCT) coding. In telephony, a standard audio signal for a single phone call is encoded as 8,000 samples per second , of 8 bits each, giving a 64 kbit/s digital signal known as DS0 . The default signal compression encoding on
3724-471: The execution of program code typically causes an instruction memory access pattern of locally consecutive addresses, bus encodings using Gray code addressing instead of binary addressing can reduce the number of state changes of the address bits significantly, thereby reducing the CPU power consumption in some low-power designs. The binary-reflected Gray code list for n bits can be generated recursively from
3800-542: The first commercial digital recordings. In 1972, 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. 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 1979,
3876-436: The first digital pop album, Bop till You Drop , was recorded. It was recorded in 50 kHz, 16-bit linear PCM using a 3M digital tape recorder. 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 disc. The rapid development and wide adoption of PCM digital telephony
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#17328561221933952-450: The form of a Gray code. Other encoders employ non-contact mechanisms based on optical or magnetic sensors to produce the Gray code output signals. Regardless of the mechanism or precision of a moving encoder, position measurement error can occur at specific positions (at code boundaries) because the code may be changing at the exact moment it is read (sampled). A binary output code could cause significant position measurement errors because it
4028-431: The information to be encoded is 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. Digital signal (signal processing) In the context of digital signal processing (DSP),
4104-448: 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
4180-418: The list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0 , prefixing the entries in the reflected list with a binary 1 , and then concatenating the original list with the reversed list. For example, generating the n = 3 list from the n = 2 list: The one-bit Gray code
4256-589: The most significant bit), and b i {\displaystyle b_{i}} is the i {\displaystyle i} th binary-coded bit ( b 0 {\displaystyle b_{0}} being the most-significant bit), the reverse translation can be given recursively: b 0 = g 0 {\displaystyle b_{0}=g_{0}} , and b i = g i ⊕ b i − 1 {\displaystyle b_{i}=g_{i}\oplus b_{i-1}} . Alternatively, decoding
4332-519: The old value or the new value is propagated. Therefore, if more than one bit in the multi-bit pointer is changing at the sampling point, a "wrong" binary value (neither new nor old) can be propagated. By guaranteeing only one bit can be changing, Gray codes guarantee that the only possible sampled values are the new or old multi-bit value. Typically Gray codes of power-of-two length are used. Sometimes digital buses in electronic systems are used to convey quantities that can only increase or decrease by one at
4408-415: The order of codewords intact if b i + 1 = 0 {\displaystyle b_{i+1}={\mathtt {0}}} , and reverses the order of blocks of 2 i + 1 {\displaystyle 2^{i+1}} codewords if b i + 1 = 1 {\displaystyle b_{i+1}={\mathtt {1}}} . Now, this is exactly the same operation as
4484-504: The order of two neighbouring codewords is reversed If bit 1 is inverted, blocks of 2 codewords change order: If bit 2 is inverted, blocks of 4 codewords reverse order: Thus, performing an exclusive or on a bit b i {\displaystyle b_{i}} at position i {\displaystyle i} with the bit b i + 1 {\displaystyle b_{i+1}} at position i + 1 {\displaystyle i+1} leaves
4560-769: 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. 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 conceived 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
4636-518: The output but are considered unlikely enough to allow reliable synchronization. In other cases, the long term DC value of the modulated signal is important, as building up a DC bias will tend to move communications circuits out of their operating range. In this case, special measures are taken to keep a count of the cumulative DC bias and to modify the codes if necessary to make the DC bias always tend back to zero. Many of these codes are bipolar codes , where
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#17328561221934712-460: The possibility that, when multiple bits change in the binary representation of a position, a misread will result from some of the bits changing before others. For example, some rotary encoders provide a disk which has an electrically conductive Gray code pattern on concentric rings (tracks). Each track has a stationary metal spring contact that provides electrical contact to the conductive code pattern. Together, these contacts produce output signals in
4788-540: 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
4864-459: The reflect-and-prefix method to generate the Gray code. A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel. Assuming g i {\displaystyle g_{i}} is the i {\displaystyle i} th Gray-coded bit ( g 0 {\displaystyle g_{0}} being
4940-564: The reflected binary code was later named after Gray by others who used it. Two different 1953 patent applications use "Gray code" as an alternative name for the "reflected binary code"; one of those also lists "minimum error code" and "cyclic permutation code" among the names. A 1954 patent application refers to "the Bell Telephone Gray code". Other names include "cyclic binary code", "cyclic progression code", "cyclic permuting binary" or "cyclic permuted binary" (CPB). The Gray code
5016-423: The same purpose, in 1874. Frank Gray , who became famous for inventing the signaling method that came to be used for compatible color television, invented a method to convert analog signals to reflected binary code groups using vacuum tube -based apparatus. Filed in 1947, the method and apparatus were granted a patent in 1953, and the name of Gray stuck to the codes. The " PCM tube " apparatus that Gray patented
5092-513: 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. The 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 multiplexing schemes. In 1973, adaptive differential pulse-code modulation (ADPCM)
5168-454: The term reflected binary code in his 1947 patent application, remarking that the code had "as yet no recognized name". He derived the name from the fact that it "may be built up from the conventional binary code by a sort of reflection process". In the standard encoding of the Gray Code the least significant bit follows a repetitive pattern of 2 on, 2 off ( … 11001100 … ); the next digit
5244-430: The transition might look like 011 — 001 — 101 — 100 . When the switches appear to be in position 001 , the observer cannot tell if that is the "real" position 1, or a transitional state between two other positions. If the output feeds into a sequential system, possibly via combinational logic , then the sequential system may store a false value. This problem can be solved by changing only one switch at
5320-563: The use of PCM for voice communication in 1937 while working for International Telephone and Telegraph in France. He described the theory and its 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,
5396-692: 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. Audio coding formats and audio codecs have been developed to achieve further compression. Some of these techniques have been standardized and patented. Advanced compression techniques, such as modified discrete cosine transform (MDCT) and linear predictive coding (LPC), are now widely used in mobile phones , voice over IP (VoIP) and streaming media . PCM can be either return-to-zero (RZ) or non-return-to-zero (NRZ). For
5472-452: The voice signal, telephony applications therefore typically use an 8000 Hz sampling frequency which is more than twice the highest usable voice frequency. Regardless, there are potential sources of impairment implicit in any PCM system: 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
5548-405: The waveform values or companded ) or floating-point words. The process of analog-to-digital conversion produces a digital signal. The conversion process can be thought of as occurring in two steps: An analog signal can be reconstructed after conversion to digital (down to the precision afforded by the quantization used), provided that the signal has negligible power in frequencies above
5624-558: Was developed, by P. Cummiskey, Nikil Jayant and James L. Flanagan . 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, engineers at Denon recorded
5700-432: Was enabled by metal–oxide–semiconductor (MOS) switched capacitor (SC) circuit technology, developed in the early 1970s. This led to the development of PCM codec-filter chips in the late 1970s. The silicon-gate CMOS (complementary MOS) PCM codec-filter chip, developed by David A. Hodges and W.C. Black in 1980, has since been the industry standard for digital telephony. By the 1990s, telecommunication networks such as
5776-465: Was made by Raymond W. Sears of Bell Labs, working with Gray and William M. Goodall, who credited Gray for the idea of the reflected binary code. Gray was most interested in using the codes to minimize errors in converting analog signals to digital; his codes are still used today for this purpose. Gray codes are used in linear and rotary position encoders ( absolute encoders and quadrature encoders ) in preference to weighted binary encoding. This avoids
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