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Quantization (signal processing)
In digital signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values; that is, converting an analog signal to a digital one via analog-to-digital conversion. In general, a quantization operator can be represented as
where x is a real number, Q(x) an integer, and f(x) is an arbitrary real-valued function that controls the "quantization law" of the particular coder.
In computer audio, a linear scale is most common. If x is a real valued number between -1 and 1, the quantization operator can therefore be alternately expressed as,
where M is the number of bits used to quantize the value. Using this quantization law and assuming that quantization noise is uniformly distributed (accurate for rapidly varying x or high M), the signal to noise ratio can be approximated as
From this equation, it is often said that the SNR is approximately 6dB per bit.
In digital telephony, two popular quantization schemes are the 'A-law' (dominant in Europe) and 'µ-law' (dominant in North America and Japan). These schemes map discrete analog values to an 8 bit scale that is nearly linear for small values and then increase logarithmically as amplitude grows. Because the human ear's perception of loudness is roughly logarithmic, this provides a higher signal to noise ratio over the range of audible sound intensities for a given number of bits.
- Analog-to-digital converter, Digital-to-analog converter
- Discrete, Digital
- Information theory
- Rate distortion theory
- Vector quantization
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