Note that if the commonly used FOH (or ZOH) were chosen as the intersample behaviour of the signals when discretising the prefilters, the reconstruction of $u(t)$ would suffer from high frequency distortion, which usually leads to inaccuracies in the computation of $\varphi_f(t_k)$ and $\hat{\varphi}_f(t_k)$. As stated next, only an inaccurate computation of the regressor vector $\varphi_f(t_k)$ causes generic inconsistency of the proposed method under CT multisine input excitation.

**.** Assume that an incorrect intersample behaviour in the input signal is assumed, but nevertheless satisfies $G(p)u(t_k) = \{G(p)u(t)\}_{t_k}$ as $h\to 0$. The SRIVC-type estimator with filtered regressor and instrument vectors given by and respectively

1.  remains generically consistent if an incorrect assumption on the intersample behaviour is used for generating the filtered signals in the instrument vector $\hat{\varphi}_f(t_k)$, and

2.  is generically inconsistent if an incorrect assumption on the intersample behaviour is used for filtering the input signal in the regressor vector $\varphi_f(t_k)$.

[Proof.]{}

*Statement 1*: The result follows from the same logic as in the proof in [@pan2020consistency Corollary 3, Statement 1].

*Statement 2*: Statement 1 of Theorem \[theorem1\] still holds by following the same steps as before, but this time the vector $\Delta(t_k)$ in will also have non-zero elements 