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[[da:Kvantisering]]▼
[[Category:Signal processing]]▼
[[Image:FloorQuantizer.png|right|frame|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
In general, a quantization operator can be represented as :<math>Q(x) = \operatorname{round}(f(x))</math>
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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) = \frac{\operatorname{round}(2^{M-1}x)
where 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 ''x'' or high ''M''), the [[signal to noise ratio]] can be approximated as
:<math>
From this equation, it is often said that the SNR is approximately 6dB per bit.
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In digital [[telephone|telephony]], two popular quantization schemes are the '[[A-law algorithm|A-law]]' (dominant in [[Europe]]) and '[[Mu-law algorithm|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.
==See also
*[[Analog to digital conversion]], [[Digital to analog conversion]]
*[[Discrete]], [[Digital]]
*[[Dither]]▼
*[[Information theory]]
*[[Rate distortion theory]]
*[[Vector quantization]]
▲*[[Dither]]
▲[[Category:Signal processing]]
▲[[da:Kvantisering]]
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