In the following, we say that a *correct intersample behaviour in the input signal is assumed* whenever the intersample behaviour of such signal in the SRIVC algorithm matches that of the system input. In [@pan2020consistency] it was shown that the SRIVC estimator

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 $\varphi_f(t_k)$.

This result indicates that the intersample behaviour of the input signal needs to be correctly taken into account for the consistency of the SRIVC estimator. In particular, it implies that if the system input is a signal that is not produced by a hold mechanism, the estimator will be generically inconsistent. This argument holds regardless of whether the additive noise $v(t_k)$ is white or coloured.

Consistent SRIVC-type method {#sec4}
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As mentioned in the previous section, a correct assumption of the intersample behaviour of the input (ZOH of FOH) in the regressor vector $\varphi(t_k)$ guarantees generic consistency under mild conditions. The extension of this principle constitutes our main contribution. 