 Quantization of x using Q(x) = floor(Lx)/L. 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
- <math>Q(x) = \operatorname{round}(f(x))<math>
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,
- <math>Q(x) = \frac{\operatorname{round}(2^{M-1}x)}{2^{M-1}}<math>
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
- <math>\frac{S}{N_q} \approx (6.02M + 1.76)dB<math>.
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.
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