Does anyone now the coding for de-quantization?

Does anyone now the coding for de-quantization? Simply saying, does anyone how to get back original signal after quantization?

Answer 1

[Image Analyst]

If you've lost it, then you can't get it back. If I have a thousand numbers with values going between 0 and 100, and I quantize it to three levels - 0, 50, and 100 - then there is no way I can get back the original numbers. For example if element 672 originally had a value of 60, and then got quantized to 50, how would you ever know that it originally was 60 if all you had was 50? You wouldn't, unless you saved the original.

Answer 2

[Walter Roberson]

Take all oc of your numbers and quantize them each to be 0 or 1. Now take all of the bits that result and put them together in sequence to form one binary number. Now quantize that binary number down to 0 or 1.

We have started with an arbitrary long sequence of numbers and we have arrived at a single bit.

Now you have a thesis that given a set of quantized values that it is possible to recover the exact original value. So apply your hypothetical recovery method to the single bit. If you are correct then you can get back the exact long binary number. Split that number into individual bits and apply your hypothetical recovery method, getting back each individual number.

Thus if your thesis is correct, then any sequence of numbers can be fully recovered from a single bit.

Now I want you to consider the three distinct sequences, {1}, {2}, and {3}. One of the first two will resolve down to the bit 0. The other of the first two will resolve down to the bit 1 (because if they both resolved to 0 or 1 then you would not be able to tell them apart). So now a question for you: what does the third sequence resolve to? If it resolbes to 0 then you cannot tell it apart from one of the first two. If it resolves to 1 then you cannot tell it apart from the other. But your hypothesis is that we can quantize arbitrarily and fully recover the original values.

We have arrived at a contradiction, and therefore your thesis must be false: what you ask for cannot be done.