Is it possible to estimate variance of noise for a step answer signal? I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. 

So assume that we have a signal which look like this:



The clean signal is $y(t)$ and the noise is $e(t)$. In this case, $e(t)$ has the variance 1 because it's generated by Octave/MATLAB function 0.05*randn(). 

So my question is:
How can i estimate variance of this noise from this signal?
Hi: In order to estimate the variance, you need to have an underlying model for your signal. So, suppose that the model is

$y_{t+1} = y_t + \epsilon_t$ $~\forall ~ t = 1,\ldots n $.

assuming that $E(\epsilon_t) = 0$ and $var(\epsilon_t) = \sigma^2$.

In this case, you would difference your data in order to get estimates
of  $\epsilon_{t}$ at each time $t$, and call the estimates 
$\hat{\epsilon}_t, ~\forall i = 2, \ldots n$.

Then, then an unbiased estimate of $\sigma^2 , \hat{\sigma}^2$, $= \frac{1}{n-2} \sum_{i=2}^{n}  (\hat{\epsilon_i} - 0)^2$.

But that estimate is critically dependent on the assumed model for the response $y_{t}$ ( this model is sometimes used in finance for the log price at time t+1 and is referred to as a random walk model ).  A different model will lead to a different estimate of the noise because the assumptions about the noise will be quite different in each case. I hope this helps some.