Talk:Quantization (signal processing)

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[edit] Several comments on page

I am not an expert with Wiki markup, so I do not plan to edit the page directly. However, I have some brief comments/opinions that may be of interest to the next person who decides to edit this page: klm 1. I think the basic description of "quantization" could use a little bit of tweaking. The current definition is: "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." I believe that the definition could be made more precise: "quantization is the non-reversible process of approximating a value to one of a countable set of values." Then, specify that the original value can be from a continuous and uncountable domain, and can be multi-dimensional (i.e. vector vs. scalar quantization). The. ;,lpjkjh problem with the current definition is that the set that is mapped to by the quantizer does not necessarily have to be "small". In fact, the set being mapped to could have infinite cardinality. The only restriction that is placed on a quantizer is that the range of values being mapped must be countable.. i.e. mappable to the set of integers in some way.

2. I disagree with the floor in the scalar quantization function. It is not correct to say that scalar quantizers perform a floor.

3. Some examples will be useful for non-technical readers. I would recommend the classical "round to the nearest integer" example, as well as an example with non-uniform scalar quantization. The non-uniform quantizer doesn't have to be useful in practice, but it is to open the mind of many readers who might think a quantizer must always "round" in some regular fashion.

4. Demonstrate that quantization is non-reversible by stating a simple example: For the "rounding to the nearest integer quantizer", demonstrate that the quantizer would round 2.6, 2.8, 2.95, 3.3 all to the value of 3. But given (only) the quantized value of 3, there is no way of recovering what the original value was. This is an important issue for lossy compression.

—Preceding unsigned comment added by 70.187.205.90 (talk • contribs) 02:37, 30 January 2006

[edit] Definition of floor function

To stress that the transition from continuous to discrete data is achieved by the floor function, it might be useful to require f to be continuous. Additionally, I think

is confusing, it may be better to use \lfloor y \rfloor or \lfloor \cdot \rfloor instead of \lfloor x \rfloor.

--134.109.80.239 14:50, 11 October 2006 (UTC)

I liked your \lfloor \cdot \rfloor suggestion, and just put it into the article. -SudoMonas 17:22, 13 October 2006 (UTC)

[edit] Incorrect statement about quantization in nature

This page incorrectly stated that at a fundamental level, all quantities in nature are quantized. This is not true. For example, the position of a particle or an atom is not quantized, and while the energy of an electron orbiting an atomic nucleus is quantized, an electron's energy in free space is not quantized. I have changed the word "all" to "some" in the text to correct the false statement, but a much more optimal revision could be made.

71.242.70.246 18:03, 12 May 2007 (UTC)