edVirtus Reference

What Is Companding?

What Are μ-law and A-law Companding?

Preview: Learn more about companding and how it improves the quality of digitally encoded analog signals.

Companding is a signal-processing technique used to improve the quality of digitally encoded analog signals, particularly speech. The term companding is a contraction of the words compressing and expanding. Before transmission or analog-to-digital conversion, the signal is compressed so that weak signals occupy a larger proportion of the available dynamic range. After reception, the reverse process—expansion—restores the signal to its original amplitude characteristics. Companding significantly reduces the effects of quantization noise without increasing the number of bits required to represent each sample.

The need for companding arises because many real-world signals have a very wide range of amplitudes. Human speech provides a good example. During a conversation, some sounds may be extremely quiet while others are much louder. If all amplitudes are quantized using equally spaced levels, as in a uniform quantizer, the quantization error remains approximately constant regardless of signal level. Consequently, the error represents only a tiny fraction of a loud signal but may become comparable to a weak signal, producing noticeable distortion or background noise.

Companding addresses this problem by using a nonlinear relationship between the input signal and the quantization levels. Before quantization, small-amplitude signals are amplified relative to large-amplitude signals by a compression process. This effectively provides many closely spaced quantization levels for weak signals and fewer, more widely spaced levels for strong signals. As a result, low-level speech is represented much more accurately than would be possible using uniform quantization with the same number of bits.

At the receiver, the complementary expander reverses the compression process. Large and small signals are restored to their original relative amplitudes, while the quantization noise introduced during analog-to-digital conversion remains approximately unchanged. Because the weak signals were represented more accurately during quantization, the recovered speech exhibits a significantly higher perceived signal-to-noise ratio than would otherwise be obtained.

One useful analogy is to imagine taking a photograph in which the shadows contain much more important detail than the bright sky. Rather than allocating equal precision to every brightness level, a photographer might deliberately devote more of the camera's available tonal range to the darker regions where detail is most difficult to preserve. Companding performs a similar function for electrical signals, allocating more quantization precision where it is most beneficial.

Two principal companding standards are used throughout the world. μ-law (mu-law) companding is employed primarily in North America and Japan, while A-law companding is used throughout most of Europe and many other countries. Both techniques perform the same fundamental function but employ slightly different mathematical compression characteristics. Despite these differences, each provides a substantial improvement in the perceived quality of digitally encoded speech compared with uniform quantization.

Companding played a crucial role in the development of Pulse Code Modulation (PCM) telephony. Early digital telephone systems typically represented speech using only eight bits per sample, providing 256 quantization levels. Without companding, this limited resolution would have produced objectionable distortion during quiet speech. By applying μ-law or A-law compression before quantization, telephone systems achieved excellent voice quality while maintaining the standard transmission rate of 64 kb/s that became widely adopted throughout the world's telephone networks.

It is important to distinguish companding from data compression. Companding changes the relationship between signal amplitude and quantization level to improve signal quality, but it does not reduce the number of transmitted bits. Data compression, by contrast, seeks to reduce the amount of information transmitted or stored by removing redundancy from the signal. The two techniques serve entirely different purposes, although both involve the word compression.

Although originally developed for digital telephony, companding continues to be used in many other applications. Audio recording, voice-over-IP systems, digital radio, instrumentation, and various signal-processing systems employ nonlinear quantization techniques based on the same underlying principles. More sophisticated adaptive quantization methods have since been developed, but the concept of allocating greater precision to weaker signals remains fundamental to many modern coding systems.

Today, companding remains one of the classic techniques of communications engineering. By recognising that human perception is much more sensitive to noise during quiet passages than during loud ones, engineers were able to improve the quality of digitally encoded speech dramatically without increasing transmission bandwidth. This elegant solution allowed digital telephony to become both practical and economical and continues to influence the design of modern analog-to-digital conversion systems.