Reconstruction of a quantizied signal. (Signal Theory & Sampling)

We have the signal f( x ) = a.

Oversample this signal by a factor of two.

Let's say we model this problem as the projection of the signal up too

the frame bound F = (e1 e2)' ( ' = transposed).

The samplingnoise can be modeled as an addition of noise n, which is white noise (that is temporarly uncorrelated and with mean zero) and has the variance = 2. In other words we get Ff(x) = (a + n1 a + n2)'.

Problem:

Show for this case that the reconstruction leads two a decrease of the power of the noise for the reconstructed signal. Which reduction av the noise is it?

Mvh

Rikard

Ps. This is for school so a well described solution is prefered so that I actually learn something instead of just getting the answer. dS