Quantization (signal processing): Difference between revisions

Revision as of 03:38, 8 October 2004

Revision as of 03:52, 8 October 2004

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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) = \operatorname{floor}(2^{M-1}x)/2^{M-1}</math>

where ''floor()'' returns the highest integer less than or equal to x and M is the number of bits used to quantize the value. Using this quantization law and assuming that quantization noise is [[uniform distribution|uniformly distributed]] (accurate for rapidly varying ''xx'' or high ''M''), the [[signal to noise ratio]] can be approximated as

:<math>\begin{matrix}\frac{S}{N_q}\end{matrix} =\approx (6.02M + 1.76)dB</math>.

From this equation, it is often said that the SNR is approximately 6dB per bit.

In digital [[telephone|telephony]], two popular quantization schemes are the '[[A-law algorithm|A-law]]' (dominant in [[Europe]]) and '[[Mu-law algorithm|&micro;-law]]' (dominant in [[North America]] and [[Japan]]). These schemes map adiscrete linearlyanalog quantized 14 bit integer valuevalues to an 8 bit scale. The scalethat 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 providing a greaterhigher signal to noise ratio over dynamicthe range thanof audible sound intensities for a purelygiven linearnumber scaleof bits.

See also: