System Identification - Mathematical expression for a signal
In your upper path, the transfere function of \$H(z)\$ uses the actual input sample at time \$n_0\$ and the next sample at time \$n_{1}\$
Also, \$F_{2}(Z)\$ processes the delayed samples of \$H(z)\$. Therefore we need to define the input as a Matrix in form of delayed input vectors for \$H(z)\$

\$w[n]={\begin{bmatrix}
w_0 &amp; w_{-1}\\ 
w_{-1} &amp; w_{-2}\\ 
w_{-2} &amp; w_{-3}
\end{bmatrix}}\$

For \$n_0\$ we get following expression:
\$d[n]=\mathbf{f_2}\cdot(\mathbf{w}[n] \cdot \mathbf{h^T}+ \mathbf{v}[n])\$

And this gives:
\$d[n]=\begin{bmatrix}
0 &amp; 1 &amp; 0.1
\end{bmatrix}\cdot(\begin{bmatrix}
w_0 &amp; w_{-1}\\ 
w_{-1} &amp; w_{-2}\\ 
w_{-2} &amp; w_{-3}
\end{bmatrix}\cdot\begin{bmatrix}
3\\ 
2
\end{bmatrix} + \begin{bmatrix}
v_0\\ 
v_{-1}\\ 
v_{-2}
\end{bmatrix})\$

which outputs a scalar for \$d[n]\$