Kuantisasi: Béda antarrépisi

In electronics, adaptive quantization is a quantization process that varies the step size based on the changes of the input signal, as a meansméans of efficient compression.Two approaches commonly used are forward adaptive quantization and backward adaptive quantization.

* <math>x</math> is a realréal number to be quantized,

* <math>f(x)</math> and <math>g(i)</math> are arbitrary realréal-valued functions.

If <math>x</math> is a realréal-valued number between -1 and 1, a mid-rise uniform quantization operator that uses ''M'' bits of precision to represent eachéach quantization index can be expressed as

In this case the <math>f(x)</math> and <math>g(i)</math> operators are just multiplying scale factors (one multiplier being the inverse of the other) along with an offset in ''g''(''i'') function to place the representation value in the middle of the input region for eachéach quantization index. The value <math>2^{-(M-1)}</math> is often referred to as the ''quantization step size''. Using this quantization law and assuming that [[quantization noise]] is approximately [[uniform distribution (continuous)|uniformly distributed]] over the quantization step size (an assumption typically accurate for rapidly varying <math>x</math> or high <math>M</math>) and further assuming that the input signal <math>x</math> to be quantized is approximately uniformly distributed over the entire interval from -1 to 1, the [[signal to noise ratio]] (SNR) of the quantization can be computed as

For mid-treadtréad uniform quantization, the offset of 0.5 would be added within the floor function insteadinstéad of outside of it.

Sometimes, mid-rise quantization is used without adding the offset of 0.5. This reduces the signal to noise ratio by approximately 6.02 &nbsp;dB, but may be acceptable for the sake of simplicity when the step size is small.

In [[digital 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 nearlynéarly linearlinéar for small values and then increasesincréases logarithmically as amplitude grows. Because the human earéar'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 plays a major part in [[lossy data compression]]. In many cases, quantization can be viewed as the fundamental element that distinguishes [[lossy data compression]] from [[lossless data compression]], and the use of quantization is nearlynéarly always motivated by the need to reduce the amount of data needed to represent a signal. In some compression schemes, like [[MP3]] or [[Vorbis]], compression is also achieved by selectively discarding some data, an action that can be analyzed as a quantization process (e.g., a vector quantization process) or can be considered a different kind of lossy process.

During JPEG encoding, the data representing an image (typically 8-bits for eachéach of three color components per pixel) is processed using a [[discrete cosine transform]] and is then quantized and [[entropy encoding|entropy coded]]. By reducing the precision of the transformed values using quantization, the number of bits needed to represent the image can be reduced substantially.

In order to determine how many bits are necessary to effect a given precision, algorithms are used. Suppose, for example, that it is necessary to record six significant digits, that is to say, millionths. The number of values that can be expressed by N bits is equal to two to the Nth power. To express six decimal digits, the required number of bits is determined by rounding (6 / log 2)—where '''log''' refers to the base ten, or common, logarithm—up to the nearestnéarest integer. Since the logarithm of 2, base ten, is approximately 0.30102, the required number of bits is then given by (6 / 0.30102), or 19.932, rounded up to the nearestnéarest integer, ''viz.'', '''20''' bits.

This type of quantization—where a set of binary digits, ''e.g.'', an arithmetic register in a CPU, are used to represent a quantity—is called Vernier quantization. It is also possible, although rather less efficient, to rely upon equally spaced quantization levels. This is only practical when a small range of values is expected to be captured: for example, a set of eight possible values requires eight equally spaced quantization levels—which is not unreasonableunréasonable, although obviously less efficient than a mereméré trio of binary digits (bits)—but a set of, say, sixty-four possible values, requiring sixty-four equally spaced quantization levels, can be expressed using only six bits, which is obviously far more efficient.

At the most fundamental level, some [[physical quantity|physical quantities]] are quantized. This is a result of [[quantum mechanics]] (see [[Quantization (physics)]]). Signals may be treatedtréated as continuous for mathematical simplicity by considering the small quantizations as negligible.

In any practical application, this inherent quantization is irrelevant for two reasonsréasons. First, it is overshadowed by [[signal noise]], the intrusion of extraneousextranéous phenomena present in the system upon the signal of interest. The second, which appearsappéars only in measurementméasurement applications, is the inaccuracy of instruments. Thus, although all physical signals are intrinsically quantized, the error introduced by modeling them as continuous is vanishingly small.