Quantization confusion in pulse code modulation.

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shivajikobardan

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I have a question-:
This is a quantized version of an information signal. Here number of bits used to encode is 4 so there are 16 levels.





Here is the encoding.
I tried to do this with similar type of questions.


But as you see here is the problem. There are 5 Voltage levels but only 4 possible encodings. There is a solution to this afaik it is to let like-:

4V-2V=00
2V-0V=01
0V-–2V=10
-2V- -4V=11.
But that is making less sense to me at the moment.
Can you shed some light in this issue?
 

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Hi,

I'm not able to follow your thoughts completely. But the quantization step voltage can be determined by

V_FS / (2^n) = (4 V - -4V) / 2^4 = 8 V / 16 = 0.5 V.​
​
So there are 16 quantization steps, each one covers an interval of 0.5 V. Have you choesen a 2 Bit ADC (n = 2 --> L = 4) on purpose for your pen & paper example, I assume so?

shivajikobardan said:
4V-2V=00
2V-0V=01
0V-–2V=10
-2V- -4V=11.
Click to expand...

Here you are dealing with ranges, as you have correctly shown. So there are no five specific voltages, only ranges, and of course TWO voltage levels define ONE interval/range. Consequently, you have one range less than specific voltage levels. Have a look on the links below, they might help you, especially [3].

[1] https://www.analog.com/en/education/education-library/data-conversion-handbook.html
[2] https://www.analog.com/media/en/tra...ndbooks/Data-Conversion-Handbook/Chapter2.pdf
[3] https://microchipdeveloper.com/adc:adc-quantization-error

BR
 

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Hi,

the first picture shows an "unsigend" behaviour from 0 to 15.

the second one is a signed behaviour (-4 ... 0 ... +3). But a signed behaviour is 16 steps including zero, thus just 15 steps are available for non_zero values. You can´t have symmetric behaviour, unless:
* you define the range to be -3 ... 0 ... +3 (leave the "-4" redundant)
* you define the steps to be -3.5 / -2.5 / -1.5 / -0.5 / +0.5 / ... /+3.5. But you can´t have true zero

Klaus
 

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