Content deleted Content added
moving info from Signal (information theory) |
Clarified point about discrete signal -> digital signal; other clean up |
||
Line 1:
[[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 range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values.
More specifically, a [[signal (information theory)|signal]] can be multi-dimensional and quantization need not be applied to all dimensions. A discrete signal need not necessarily be quantized (a pedantic point, but true nonetheless and can be a point of confusion). ''See [[ideal sampler]].'' A common use of quantization is in the conversion of a [[
Both of these steps (sampling and quantizing) are performed in [[analog-to-digital converter]]s with the quantization level specified A specific example would be [[compact disc]] (CD) audio which is sampled at 44,100 [[Hz]] and quantized with 16 bits (2 [[byte]]s) which can be one of 65,536 (<math>2^{16}</math>) possible values per sample.
== Mathematical description ==
The simplest and best-known form of quantization is referred to as [[scalar]] quantization, since it operates on scalar (as opposed to multi-dimensional [[vector]]) input data.
In general, a scalar quantization operator can be represented as :<math>Q(x) = g(\lfloor f(x) \rfloor)</math>
where
* <math>x</math> is a real number,
* <math>\lfloor x \rfloor</math> is the [[floor function]], yielding the integer <math>i = \lfloor f(x) \rfloor</math>
Line 57 ⟶ 61:
== External links ==
*[http://www.math.ucdavis.edu/~saito/courses/ACHA/44it06-gray.pdf Paper on mathematical theory and analysis of quantization]
[[Category:Signal processing]]
| |||