Let (\Omega , F, P)= ([0,1], \beta [0,1], dx) , where \beta is a borel set.
F_n= \sigma ([\frac{k}{2^n}, \frac{k+1}{2^n}, k=0,1,...2^n-2, [\frac{k}{2^n}, \frac{k+1}{2^n}], k=2^n-1).
f(x)=x.

Then write the explicit formula for f_n(x)=E(f|F_n)