# Modelling of quantization noise with logarithmic steps

I have to modell the quantization noise of ADC. I only know that the maximum relative error is 1 dB. Since this is logarithmic, I find it hard to formulate an appropriate model for the quantization error and noise.

Any help would be greatly appreciated!

Edit: Thanks for the input so far. As I recognize that this question is not properly formulated, I try it again:

I get measured data from a device that is the amplitude in dBm of a received signal. I know that the uncertainty is 1 dB. This being logarithmic, I guess I can't simply split it up and say that the error is uniformly distributed within a +- 0.5 dB interval?

My aim is to get a distribution that describes probable measurement results for this device if I read for example -80 dBm.

I hope this clarifies the question

• That's not a logarithmic relation at all, it just says that the error is $10^{0.05}$ relative to the full scale, or quantization step, or whatever that dB is relative to. – Marcus Müller Aug 29 '17 at 19:33
• But: I'm really confused, as your title implies your ADC is logarithmically stepped. So, I need you to confirm: What kind of ADC are we talking about? Can you link to a datasheet? – Marcus Müller Aug 29 '17 at 19:39
• Try looking at mu-law quantization (Wikipedia) and see if it provides any clarification. The log isn't appropriate for negative values and even if the input values are positive, values between 0 and 1 give negative output. – Stanley Pawlukiewicz Aug 30 '17 at 0:57