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Pulse-code modulation

PCM is a general expression for digitizing an analogue signal. A PCM signal is in fact the numerical or digital representation of the analogue signal. In most cases, the analogue signal is sampled by means of an Analog-to-Digital Converter (ADC), which is represented by this symbol:

Likewise, the signal can be converted back from the digital to the analogue domain with a Digital-to-Analog Converter (DAC). A DAC is usually represented by this symbol:

The quality of the recorded data is determined by the sample rate (T) and the bit-depth — i.e. the total number of possible different values for a single sample. For example: when using 8 bits, a total of 28 = 256 different values are available. A sample is always rounded off to the nearest bit value, which introduces an error. This error is responsible for the quantisation noise. Further­more, a low sampling rate causes a less accurate representation of the original signal, which introduces aliasing. Both effects are responsible for the amount of distortion of the signal.

Aliasing effect when sampling, caused by quantization errors

Generally speaking: the higher the bit-depth and the sampling rate, the smaller the error and the lower the distortion. The diagram below shows an arbitrary sound wave that is sampled at 'T' intervals. Move the mouse over the diagram above to see the resulting digital approximation.

Sending PCM data typically requires (at least) twice the bandwidth of the analogue original, but the quality is unsurpassed. It is suitable for speech as well as high fidelity music. PCM is very suitable for high-quality sound transmission, as long as sufficient bandwidth is available.

 PCM on Wikipedia

In practice, PCM is often combined with a compression algorithm to lower the amount of data and, hence, the bandwidth. This allows an originally wideband signal to be send over a narrow­band channel. At the receiving end, the signal must be decompressed before it can be used.

Compressing and decompressing a digital (PCM) signal

Most compression techniques not only reduce the amount of data, but also the quality of the sound. Such a technique is known as a lossy compression. In contrast, a lossless compression technique preserves the full fidelity of the orignal signal, but at the cost of a lower compression ratio. In military communications lossy compression is commonly used, such as LPC-10 or CELP.

Compressing and decompressing a digital (PCM) signal

If the transmission path is cryptographically secured, the data will usually be encrypted after compression. At the receiving end, it must then be decrypted before it can be decompressed.

In its simplest implementation, the quantization levels are linearly uniform, which means that the possible values are evently spread over the Y-axis. This is known as Linear PCM, or LPCM, al­though the term PCM is also used. High-fidelity audio systems (i.e. systems with a high bit-depth, e.g. 16 or 24 bits) generally use LPCM, as it covers the full dynamic range of the signal.

With low bit-rates the number of possible values is limited, as a result of which the audio signal cannot be accurately described. For example: with 8 bits, only 256 discrete values are possible (128 for negative amplitudes and 128 for positive amplitudes). This is particularly the case with speech, of which the wide dynamic range does not lend itself well to efficient linear digital en­co­ding. In such cases it is possible to dis­tribute the values as a function of the amplitude, like this:

Examples of non-linear distribution algorithms are A-law and µ-law. They effectively reduce the dynamic range of the signal, but increase the coding efficiency, resulting in a signal-to-distortion ratio that is superior to that obtained by linear PCM [4].

µ-law, also written as µ-law or u-law or PCMU, is a standard companding algorithm, used in American and Japanese 8-bit PCM systems. It optimises (i.e. modifies) the dynamic range of an ana­log signal for digitizing. Together with A-law it is part of the G.711 standard of the ITU-T [3].

 µ-law on Wikipedia

A-law, also known as PCMA, is a standard companding algorithm, used in European 8-bit PCM systems. Like µ-law It optimises (i.e. modifies) the dynamic range of an analog signal for digi­tizing. Together with µ-law it is part of the G.711 standard of the ITU-T [4].

 A-law on Wikipedia

Of these two companding algorithms, µ-law provides a slightly larger dynamic range than A-law, at the cost of worse proportional distorition for low-amplitude signals. In international telephony, A-law is used by convention for international connections, if one of the parties uses it.

PCM on this website
SIGSALY secure telephony system (Ciphony I)
Secure Telehone Unit STU-I (KY-70)
Speech/morse generator, Device 32620, used by Numbers Stations
Harddisc recorder used by FSB
Nagra CBR digital Covert Body Recorder
Nagra CCR covert recorder at the size of a credit card (no image available)
NEVO FX credit card recorder
Nevo Deep embeddable remote-controlled minature recorder
  1. Wikipedia, Pulse-code modulation
    Visited June 2022.

  2. Wikipedia, Sampling (signal processing)
    Visited June 2022.

  3. Wikipedia, µ-law algorithm
    Visited 8 May 2024.

  4. Wikipedia, A-law algorithm
    Visited 8 May 2024.
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Crypto Museum. Created: Wednesday 08 May 2024. Last changed: Wednesday, 08 May 2024 - 13:12 CET.
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