Understanding Companding
Companding solves a basic mismatch between real-world signals and the channels that carry them. Voice, audio, and many sensor signals have a very wide dynamic range, often 50 dB or more between the quietest and loudest passages. A uniform quantizer, however, spaces its decision levels evenly across the full-scale range, so the absolute size of each quantization step is fixed regardless of signal level. Loud signals are quantized with plenty of resolution to spare, while quiet signals may span only a handful of steps, giving them a poor signal-to-quantization-noise ratio. The result is that a linear converter wastes precision on loud passages and starves quiet ones.
A compander fixes this by warping the amplitude scale. The compressor applies a nonlinear, monotonic gain curve that is steep near zero and flattens toward full scale. Small samples receive large gain and are pushed up into regions where the quantizer steps represent a smaller percentage of the signal; large samples receive little or no extra gain. After the signal travels through the quantizer or channel, the expander applies the exact inverse curve, pulling the levels back to their true relationships. Because compression and expansion are matched inverses, the overall transfer is nominally linear, but the quantization noise has been redistributed so that it tracks signal level rather than staying constant.
Logarithmic companding laws
The most widely deployed companding curves are logarithmic, because a log law makes the signal-to-quantization-noise ratio nearly constant across a wide range of input levels. Two standards dominate digital telephony. Mu-law, with a parameter mu of 255, is used in North America and Japan, while A-law, with a parameter A of 87.6, is used across Europe and much of the rest of the world. Both are defined in the ITU-T G.711 recommendation and pack roughly 13 to 14 bits of equivalent dynamic range into an 8-bit code word at an 8 kHz sample rate.
Compression ratio and SNR behavior
The benefit of companding shows up as a flatter signal-to-noise ratio curve. With a uniform quantizer, the SNR drops about 6 dB for every halving of input amplitude. A well-designed log compander keeps the SNR almost flat over a 30 to 40 dB window of input levels, trading a small SNR penalty at the loudest levels for a large gain at the quietest ones. This is why an 8-bit companded voice channel sounds comparable to a 12 to 13 bit linear channel for speech.
Analog and RF applications
Companding is not limited to digital systems. Analog companders such as the Dolby and dbx noise-reduction systems compress program level before recording or transmission and expand on playback to push tape and channel noise below the audible floor. In two-way FM radio, syllabic companders raise low-level speech above the receiver noise floor and restore it on reception, improving intelligibility on weak links. Satellite and microwave telephony trunks have long used companding to fit many voice channels into a constrained link budget without audible degradation.
Design trade-offs
Companding is not free. The compressor and expander must be accurately matched, or the residual nonlinearity shows up as distortion and level errors. Syllabic analog companders introduce attack and release time constants that can cause noise pumping or breathing if poorly tuned. In digital systems the quantizer must use enough bits that the log law itself does not become the dominant error source. Despite these constraints, companding remains a compact, low-cost way to stretch effective resolution.
| Parameter | Typical value or range | Notes |
|---|
| Mu-law parameter (μ) | 255 | ITU-T G.711, North America and Japan |
| A-law parameter (A) | 87.6 | ITU-T G.711, Europe and elsewhere |
| Code word length | 8 bits | Standard digital telephony PCM |
| Equivalent linear resolution | 13 to 14 bits | For speech-band signals |
| Dynamic range gain | 24 to 36 dB | Versus uniform quantizer, low-level signals |
| Sample rate (telephony) | 8 kHz | 3.4 kHz voice bandwidth |
Frequently Asked Questions
What is companding?
Companding is the combination of compressing a signal's dynamic range at the transmitter and expanding it back at the receiver. The compressor applies more gain to low-level samples than to high-level ones, so quiet signals survive quantization, and the expander reverses the curve to restore the original amplitude relationship.
How does companding improve signal-to-noise ratio?
By boosting low-amplitude samples before quantization, companding raises them well above the quantizer step size, so the fixed quantization noise becomes a smaller fraction of the signal. After expansion the effective number of bits for small signals rises, which can recover roughly 24 to 36 dB of dynamic range compared with a uniform quantizer of the same word length.
What is the difference between mu-law and A-law companding?
Mu-law, used in North America and Japan with mu of 255, and A-law, used in Europe with A of 87.6, are two logarithmic companding curves standardized for 8-bit telephony. Mu-law gives slightly better small-signal performance, while A-law uses a linear segment near zero that simplifies low-level handling; both deliver about 13 to 14 bits of equivalent dynamic range in an 8-bit code.
Where is companding used in RF systems?
Companding appears in digitized voice channels, satellite and microwave telephony trunks, analog FM two-way radio scrambling and noise reduction, and the front-end conditioning of analog-to-digital converters where signals span a wide dynamic range relative to the available bit depth.