I have a signal sampled from $\mathbb{R}^2$ at a frequency of $2\text{Hz}$. It is quantized from $\mathbb{R}^2$ to $\mathbb{N}^2$, seemingly using the round operator.

How can I estimate the error variance from this setup ? I've found models for univariate signals but they don't factor in the sampling error, and I'm not sure how I can simply generalize the quantization error from $\mathbb{R}$ to $\mathbb{R}^2$.