Quantization (signal processing): Difference between revisions

Revision as of 04:38, 5 May 2005

Revision as of 18:35, 5 May 2005

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A common use of quantization is in the conversion of a [[continuous signal]] into a [[discrete signal]] by [[sample (signal)|sampling]] and then quantizing.

Both of these steps are performed in [[analog-to-digital converter]]s with the quantization level specified by a number of [[bit]]s.

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.

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.

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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.

==Quantization and Data Compression==

Quantization plays a major part in [[lossy data compression]]. Indeed, quantization can be viewed as the fundamental element that distinguishes [[lossy data compression]] from [[lossless data compression]], and the use of quantization is nearly always motivated by the need to reduce the amount of data needed to represent a signal.

Quantization also plays a part in [[lossy data compression]].

One example of such lossy a compression scheme is [[JPEG]] compression.

During compression, the coefficients of the [[discrete cosine transform]] are quantized to facilitate the [[entropy encoding]] step.

During JPEG encoding, the data representing an image (typically 8-bits for each of three color components per pixel ___location) is processed using a [[discrete cosine transform]] and is then quantized and [[entropy encoding|entropy coded]].

So by reducing the set of values (the post-quantized step of JPEG typically yields many zero values which be exploited to reduce the number of bits needed) by quantization, higher compression ratios can be achieved.

By reducing the precision of the transformed values using quantization, the number of bits needed to represent the image can be reduced substantially. For example, images can often be represented with acceptable quality using JPEG at less than 3 bits per pixel (as opposed the the typical 24 bits per pixel needed prior to JPEG compression). Indeed, even the original representation using 24 bits per pixel requires quantization for its [[pulse-code modulation|PCM]] sampling structure.

Compression of other types of data (e.g., audio or video signals) follows very similar principles. For example, [[MP3]] audio coding also involves transformation followed by quantization followed by entropy coding. For video, one additional technique (called [[motion compensation]]) is typically employed in addition to the other elements.

In modern compression technology, the [[information entropy|entropy]] of the output of a quantizer matters more than the number of possible values of its output (the number of values being <math>2^M</math> in the above example).

==See also==