# estimating the mean of constant + noise

(This is almost certainly covered in Statistics 101, but I missed that class..)

I have a real-world sampled signal $$S[t]$$ that is a constant $$\hat{S}$$ plus some noise $$\epsilon[t]$$. My goal is to find $$\hat{S}$$ with some high degree of confidence.

Intuitively: If I take one sample of $$S$$, I cannot extract $$\hat{S}$$. If I take an infinite amount of samples, I can perfectly reconstruct $$\hat{S}$$ (but that takes a while to compute ;). After $$n$$ samples, I can estimate $$\hat{S}$$, and my confidence in the estimation will increase as I take more samples.

I'd like to take enough samples so that the estimation of $$\hat{S}$$ is "good enough".

So: is there a function that describes the confidence in the estimate of $$\hat{S}$$ after $$n$$ samples?

• Do you know anything about the noise? Can you say how you'd want to measure deviation of $\hat{S}$ from the true signal' – Glen_b -Reinstate Monica Mar 17 at 12:53