# Companding

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Telecommunications and signal processing technique

A signal before (top) and after [μ-law compression](/source/%CE%9C-law_algorithm) (bottom)

In [telecommunications](/source/Telecommunications) and [signal processing](/source/Signal_processing), **companding** (occasionally called **compansion**) is a method of mitigating the detrimental effects of a channel with limited [dynamic range](/source/Dynamic_range). The name is a [portmanteau](/source/Portmanteau) of the words [compressing](/source/Dynamic_range_compression) and expanding, which are the functions of a **compander** at the transmitting and receiving ends, respectively. The use of companding allows signals with a large dynamic range to be transmitted over facilities that have a smaller dynamic range capability. Companding is employed in [telephony](/source/Telephony) and other audio applications such as professional [wireless microphones](/source/Wireless_microphone) and [analog recording](/source/Analog_recording).

## How it works

The dynamic range of a signal is compressed before [transmission](/source/Transmission_(telecommunications)) and is expanded to the original value at the receiver. The electronic circuit that does this is called a compander and works by compressing or expanding the [dynamic range](/source/Dynamic_range) of an analog electronic signal such as sound recorded by a microphone. One variety is a triplet of amplifiers: a [logarithmic amplifier](/source/Logarithmic_amplifier), followed by a variable-gain linear amplifier, and ending with an exponential amplifier. Such a triplet has the property that its output voltage is proportional to the input voltage raised to an adjustable [power](/source/Exponentiation).

Companded quantization is the combination of three functional building blocks – namely, a (continuous-domain) signal dynamic range *compressor*, a limited-range uniform quantizer, and a (continuous-domain) signal dynamic range *expander* that inverts the compressor function. This type of quantization is frequently used in telephony systems.[1][2]

In practice, companders are designed to operate according to relatively simple dynamic range compressor functions that are suitable for implementation as simple analog electronic circuits. The two most popular compander functions used for telecommunications are the [A-law](/source/A-law) and [μ-law](/source/%CE%9C-law) functions.

## Applications

Companding is used in digital telephony systems, compressing before input to an [analog-to-digital converter](/source/Analog-to-digital_converter), and then expanding after a [digital-to-analog converter](/source/Digital-to-analog_converter). This is equivalent to using a non-linear ADC as in a [T-carrier](/source/T-carrier) telephone system that implements [A-law](/source/A-law) or [μ-law](/source/%CE%9C-law) companding. This method is also used in digital file formats for better [signal-to-noise ratio](/source/Signal-to-noise_ratio) (SNR) at lower bit depths. For example, a linearly encoded 16-bit [PCM](/source/PCM) signal can be converted to an 8-bit [WAV](/source/WAV) or [AU](/source/Au_file_format) file while maintaining a decent SNR by compressing before the transition to 8-bit and expanding after conversion back to 16-bit. This is effectively a form of lossy [audio data compression](/source/Audio_data_compression).

Professional [wireless microphones](/source/Wireless_microphone) do this since the dynamic range of the microphone audio signal itself is larger than the dynamic range provided by radio transmission. Companding also reduces the noise and crosstalk levels at the receiver.[3]

Companders are used in concert audio systems and in some [noise reduction schemes](/source/Noise_reduction_scheme).

## History

The use of companding in an analog picture transmission system was patented by A. B. Clark of [AT&T](/source/American_Telephone_%26_Telegraph) in 1928 (filed in 1925):[4]

In the transmission of pictures by electric currents, the method which consists in sending currents varied in a non-linear relation to the light values of the successive elements of the picture to be transmitted, and at the receiving end exposing corresponding elements of a sensitive surface to light varied in inverse non-linear relation to the received current.

— A. B. Clark patent

In 1942, Clark and his team completed the [SIGSALY](/source/SIGSALY) secure voice transmission system that included the first use of companding in a PCM (digital) system.[5]

In 1953, B. Smith showed that a nonlinear DAC could be complemented by the inverse nonlinearity in a [successive-approximation ADC](/source/Successive-approximation_ADC) configuration, simplifying the design of digital companding systems.[6]

In 1970, H. Kaneko developed the uniform description of segment (piecewise linear) companding laws that had by then been adopted in digital telephony.[7]

In the 1980s and 1990s, many of the music equipment manufacturers ([Roland](/source/Roland_Corporation), [Yamaha](/source/Yamaha_Corporation), [Korg](/source/Korg)) used companding when compressing the library waveform data in their [digital synthesizers](/source/Digital_synthesizer). However, exact algorithms are unknown, neither if any of the manufacturers ever used the Companding scheme which is described in this article. The only known thing is that manufacturers did use data compression[8] in the mentioned time period and that some people refer to it as *companding* while in reality it might mean something else, for example data compression and expansion.[9] This dates back to the late '80s when memory chips were often one of the most costly components in the instrument. Manufacturers usually quoted the amount of memory in its compressed form: i.e. 24 MB of physical waveform ROM in a [Korg Trinity](/source/Korg_Trinity) is actually 48 MB when uncompressed. Similarly, Roland SR-JV expansion boards were usually advertised as 8 MB boards with '16 MB-equivalent content'. Careless copying of this technical information, omitting the *equivalence* reference, can often cause confusion.

## References

1. **[^](#cite_ref-Bennett_1-0)** W. R. Bennett, "[Spectra of Quantized Signals](http://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-3-446.pdf)", *[Bell System Technical Journal](/source/Bell_System_Technical_Journal)*, Vol. 27, pp. 446–472, July 1948.

1. **[^](#cite_ref-GrayNeuhoff_2-0)** [Robert M. Gray](/source/Robert_M._Gray) and David L. Neuhoff, "Quantization", *[IEEE Transactions on Information Theory](/source/IEEE_Transactions_on_Information_Theory)*, Vol. IT-44, No. 6, pp. 2325–2383, Oct. 1998. [doi](/source/Doi_(identifier)):[10.1109/18.720541](https://doi.org/10.1109%2F18.720541)

1. **[^](#cite_ref-3)** [A description of companding in wireless microphones](http://www.audio-technica.com/cms/site/490e7be64dfcaa53/index.html)

1. **[^](#cite_ref-4)** [US patent](https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US), A. B. Clark, "[Electrical picture-transmitting system](https://patents.google.com/patent/US1691147)", issued 13 November 1928, assigned to AT&T

1. **[^](#cite_ref-5)** Randall K. Nichols and Panos C. Lekkas (2002). [*Wireless Security: Models, Threats, and Solutions*](https://archive.org/details/wirelesssecurity00nich). McGraw-Hill Professional. p. [256](https://archive.org/details/wirelesssecurity00nich/page/256). [ISBN](/source/ISBN_(identifier)) [0-07-138038-8](https://en.wikipedia.org/wiki/Special:BookSources/0-07-138038-8). companding a-b-clark pcm.

1. **[^](#cite_ref-6)** B. Smith, "Instantaneous Companding of Quantized Signals," *Bell System Technical Journal*, Vol. 36, May 1957, pp. 653–709.

1. **[^](#cite_ref-7)** H. Kaneko, "A Unified Formulation of Segment Companding Laws and Synthesis of Codecs and Digital Compandors," *Bell System Technical Journal*, Vol. 49, September 1970, pp. 1555–1558.

1. **[^](#cite_ref-8)** ["Gearspace - View Single Post - Why is My Hardware Sampler Sounding Better Than My Software Sampler!? Same Samples!."](https://gearspace.com/board/showpost.php?p=5446278&postcount=130) *gearspace.com*. Retrieved 25 October 2024.

1. **[^](#cite_ref-9)** ["Gearspace - View Single Post - Roland JV-1080 vst plugin"](https://gearspace.com/board/showpost.php?p=13068220&postcount=146). *gearspace.com*. Retrieved 25 October 2024.

## External links

Look up ***[companding](https://en.wiktionary.org/wiki/companding)*** in Wiktionary, the free dictionary.

- [Companding: Logarithmic Laws, Implementation, and Consequences](https://www.allaboutcircuits.com/technical-articles/companding-logarithmic-laws-implementation-and-consequences/)

- [Compander Implementation in C Language for microcontrollers (open-source)](https://github.com/deftio/companders)

v t e Data compression methods Lossless type Entropy Adaptive coding Arithmetic Asymmetric numeral systems Golomb Huffman Adaptive Canonical Modified Range Shannon Shannon–Fano Shannon–Fano–Elias Tunstall Unary Universal Exp-Golomb Fibonacci Gamma Levenshtein Dictionary Byte-pair encoding Lempel–Ziv 842 LZ4 LZJB LZO LZRW LZSS LZW LZWL Snappy Other BWT CTW CM Delta Incremental DMC DPCM Grammar Re-Pair Sequitur LDCT MTF PAQ PPM RLE Hybrid LZ77 + Huffman Deflate LZX LZS LZ77 + ANS LZFSE LZ77 + Huffman + ANS Zstandard LZ77 + Huffman + context Brotli LZSS + Huffman LHA/LZH LZ77 + Range LZMA LZHAM RLE + BWT + MTF + Huffman bzip2 Lossy type Transform Discrete cosine transform DCT MDCT DST FFT Wavelet Daubechies DWT SPIHT Predictive DPCM ADPCM LPC ACELP CELP LAR LSP WLPC Motion Compensation Estimation Vector Psychoacoustic Audio Concepts Bit rate ABR CBR VBR Companding Convolution Dynamic range Latency Nyquist–Shannon theorem Sampling Silence compression Sound quality Speech coding Sub-band coding Codec parts A-law μ-law DPCM ADPCM DM FT FFT LPC ACELP CELP LAR LSP WLPC MDCT Psychoacoustic model Image Concepts Chroma subsampling Coding tree unit Color space Compression artifact Image resolution Macroblock Pixel PSNR Quantization Standard test image Texture compression Methods Chain code DCT Deflate Fractal KLT LP RLE Wavelet Daubechies DWT EZW SPIHT Video Concepts Bit rate ABR CBR VBR Display resolution Frame Frame rate Frame types Interlace Video characteristics Video quality Codec parts DCT DPCM Deblocking filter Lapped transform Motion Compensation Estimation Vector Wavelet Daubechies DWT Theory Compressed data structures Compressed suffix array FM-index Entropy Information theory Timeline Kolmogorov complexity Prefix code Quantization Rate–distortion Redundancy Symmetry Smallest grammar problem Community Hutter Prize People Mark Adler David A. Huffman Phil Katz

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