Pulse-code modulation.docx

Pulse-code modulationPulse-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) codePCM has been used in digital telephone systems and 1980s-era electronic musical keyboardsIt is also the standard form for digital audio in computers and the compact disc red book formatIt is also standard in digital video，for example，using ITU-R BT601Uncompressed 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 highModulationIn the diagram，a sine wave (red curve) is sampled and quantized for pulse code modulationThe sine wave is sampled at regular intervals，shown as ticks on the x-axisFor 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)This produces a fully discrete representation of the input signal (shaded area) that can be easily encoded as digital data for storage or manipulationFor 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，etcEncoding these values as binary numbers would result in the following set of nibbles:0111，1001，1011，1100，1101，1110，1110，1111，1111，1111，1110，etcThese digital values could then be further processed or analyzed by a purpose-specific digital signal processor or general purpose CPUSeveral Pulse Code Modulation streams could also be multiplexed into a larger aggregate data stream，generally for transmission of multiple streams over a single physical linkOne technique is called time-division multiplexing，or TDM，and is widely used，notably in the modern public telephone systemAnother technique is called Frequency-division multiplexing，where the signal is assigned a frequency in a spectrum，and transmitted along with other signals inside that spectrumCurrently，TDM is much more widely used than FDM because of its natural compatibility with digital communication，and generally lower bandwidth requirementsThere are many ways to implement a real device that performs this taskIn 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)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 sortDemodulationTo produce output from the sampled data，the procedure of modulation is applied in reverseAfter each sampling period has passed，the next value is read and a signal is shifted to the new valueAs a result of these transitions，the signal will have a significant amount of high-frequency energyTo smooth out the signal and remove these undesirable aliasing frequencies，the signal would be passed through analog filters that suppress energy outside the expected frequency range (that is，greater than the Nyquist frequency fs/2)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 filter required for anti-aliasing is much simplerIn some systems，no explicit filtering is done at all; as its 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 precisionThe 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 bandsThe electronics involved in producing an accurate analog signal from the discrete data are similar to those used for generating the digital signalThese devices are DACs (digital-to-analog converters)，and operate similarly to ADCsThey produce on their output a voltage or current (depending on type) that represents the value presented on their inputsThis output would then generally be filtered and amplified for useLimitationsThere are two sources of impairment implicit inany 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( Fs being the sampling frequency) being distorted or lost completely ( aliasing error).(One half the sampling frequencies are known as the Nyquist frequency.)Digitization as part of the PCM processIn conventional PCM，the analog signal may be processed (eg by amplitude compression)before being digitizedOnce the signal is digitized，the PCM signal is usually subjected to further processing (eg digital data compression)PCM with linear quantization is known as Linear PCM (LPCM)Some forms of PCM combine signal processing with codingOlder 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 domainThese simple techniques have been largely rendered obsolete by modern transform-based audio compression techniquesDPCM encodes the PCM values as differences between the current and the predicted valueAn algorithm predicts the next sample based on the previous samples，and the encoder stores only the difference between this prediction and the actual valueIf the prediction is reasonable，fewer bits can be used to represent the same informationFor audio，this type of encoding reduces the number of bits required per sample by about 25% compared to PCMAdaptive 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 ratioDelta modulation is a form of DPCM which uses one bit per sampleIn 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 DS0The default signal compression encoding on a DS0 is either -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 valueThis system is described by international standard G711An alternative proposal for a floating point representation，with 5-bit mantissa and 3-bit radix，was abandonedWhere circuit costs are high and loss of voice quality is acceptable，it sometimes makes sense to compress the voice signal even furtherAn ADPCM algorithm is used to map a series of 8-bit -law or A-law PCM samples into a series of 4-bit ADPCM samplesIn this way，the capacity of the line is doubledThe technique is detailed in the G726 standardLater it was found that even further compression was possible and additional standards were publishedSome 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 holdersSome ADPCM techniques are used in Voice over IP communicationsEncoding for transmissionPulse-code modulation 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 zeroesFor binary PCM systems，the density of 1-symbols is called ones-densityOnes-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 channelIn other cases，extra framing bits are added into the stream which guarantee at least occasional symbol transitionsAnother 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 st