in its bottom $m+1$ entries. Namely, the $i$-th component of $\Delta(t_k)$, with $i=n+1,\dots,n+m+1$, is now $$\Delta_i(t_k) = \frac{p^{m+n+1-i}}{A_j(p)}u(t_k)-\left\{\frac{p^{m+n+1-i}}{A_j(p)}u(t)\right\}_{t_k}, \notag$$ which still satisfies $\Delta_i(t_k)\to 0$ as $h\to 0$. Thus, Theorem \[theorem1\] is valid for this case as well. However, Statement 2 of Theorem \[theorem1\] does not yet hold. This fact follows from the same analysis done in the proof in [@pan2020consistency Corollary 3, Statement 2].

**.** A similar procedure to and could be proposed for the computation of $y_f(t_k)$ by exploiting the fact that the noiseless output also corresponds to a multisine (thus, a more adequate reconstruction scheme could be designed). However, Remark 5 of [@pan2020consistency] suggests that, as the number of iterations tends to infinity, the GEE at the converging point does not depend on the intersample behavior of the output. Thus, if the iterations converge, a more precise filtering of the output is not needed.

Extension to arbitrary input signals {#arbitrary}
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The previous method is naturally suited for multisine inputs due to the simplicity of the filtered outputs at stationary regime, since they are also multisine signals. By introducing a Delta transform description, the computations in and can be generalised for an arbitrary input signal with arbitrary accuracy. 