Is it possible to estimate variance of noise for a step answer 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.