Encoding law
In digital communications, an encoding law (or quantization law) is a (typically non-uniform) allocation of quantization levels across the possible analog signal levels in an analog-to-digital converter (ADC) system. These laws are especially important in voice encoding, where they help optimize signal-to-noise ratio and bandwidth usage.[1]
Encoding laws can be viewed as a simple form of instantaneous companding, a process that compresses the dynamic range of a signal before quantization and expands it after reconstruction.[2] This technique improves the performance of systems where the signal amplitude distribution is not uniform.
Common Encoding Laws
[edit]The two most widely used encoding laws are:
- μ-law (mu-law): Used mainly in North America and Japan. It offers better dynamic range at low amplitudes by applying a logarithmic compression function. Its mathematical formula is defined as:
: F(x) = sign(x) · ln(1 + μ|x|) / ln(1 + μ), where 0 ≤ |x| ≤ 1 and μ = 255.[3]
- A-law: Preferred in Europe and most of the rest of the world. It applies a piecewise linear-logarithmic compression function with μ ≈ 87.6.
Both encoding laws are defined in the ITU-T standard G.711, which specifies pulse code modulation (PCM) at a bit rate of 64 kbit/s for digital telephony systems.[4]
Applications
[edit]Encoding laws are essential in:
- Digital telephony
- Voice over IP (VoIP) protocols
- Speech coding and audio compression
- Legacy PSTN systems
- Embedded DSP chips and audio codecs[5]
These laws allow for a more efficient use of limited bandwidth in systems where human speech is the primary signal, as most voice energy is concentrated at low amplitudes.
Technical Rationale
[edit]Human hearing is more sensitive to changes in low-level signals than high-level signals. Encoding laws exploit this non-linearity by assigning more quantization levels to lower amplitude signals, thus improving perceptual audio quality.[6]
This is a form of **non-uniform quantization**, which provides higher resolution where it matters most. Without such companding laws, a linear quantizer would require more bits to achieve the same subjective quality.
See also
[edit]- Quantization (signal processing)
- Companding
- Pulse-code modulation
- Digital signal processing
- G.711
- Audio codec
- ITU-T
References
[edit]- ^ Proakis, John G.; Manolakis, Dimitris G. (2007). Digital Signal Processing: Principles, Algorithms, and Applications. Pearson. p. 1056. ISBN 9780131873742.
- ^ Oppenheim, Alan V.; Schafer, Ronald W. (2009). Discrete-Time Signal Processing (3rd ed.). Pearson. ISBN 9780131988422.
- ^ Jayant, N. S.; Noll, Peter (1984). Digital Coding of Waveforms: Principles and Applications to Speech and Video. Prentice Hall. p. 180. ISBN 9780132119139.
- ^ "Pulse code modulation (PCM) of voice frequencies – ITU-T Recommendation G.711". International Telecommunication Union. Retrieved 2025-06-23.
- ^ "Companding in Digital Audio Systems". Analog Devices. Retrieved 2025-06-23.
- ^ Fischer, Robert (1991). "Precoding and Signal Shaping for Digital Transmission". IEEE Communications Magazine. 29 (12): 26–34. doi:10.1109/35.103855.
 | This article related to telecommunications is a stub. You can help Wikipedia by expanding it. |