Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation.

It is defined as:

$$Q = \dfrac {\Delta x}{2^{N+1}}$$

where $N$ is the number of bits used for quantization in a analog to digital conversion, and $\Delta x$ is, in portuguese "Faixa de Excursão do Sinal", I don't know what would be the correct translation, but I bet on something like "Signal Excursion Band". I know, its a strange name.

Can someone help me with this? What is this $\Delta x$? Sorry for my bad english, it isnt my native language.

share|improve this question
Evidently you are learning the basics. Speaking as a retired EE; real designs are a lot more complicated. The answer below is idealized for discussion. While not wrong, there are large confounding terms in physical implementation. – rrogers Dec 30 '15 at 14:42
up vote 4 down vote accepted

When you quantize a signal, you introduce and error which can be defined as $$q[n] = x_q[n]-x[n]$$ where $q[n]$ is the quantization error, $x[n]$ the original signal, and $x_q[n]$ of the quantized signal. The maximum quantization error is simply $max(\left | q \right |)$, the absolute maximum of this error function. Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \frac{max(x)-min(x)}{2^{N+1}}$$

Let's look at a quick example. Let's assume you have a signal that's uniformly distributed between -1 and +1 and you want to quantize this with 3 bits. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. The difference between steps is 0.25. If you round during quantization the maximum error will be half of that (i.e. 0.125).

Now let's try the formula: $$Q = \frac{max(x)-min(x)}{2^{N+1}} = \frac{1-(-1)}{2^{3+1}}= \frac{2}{16} = 0.125$$

share|improve this answer
i found the answer before and forget to come check here. Thanks anyway! – Diedre Jun 8 '14 at 18:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.