In this work, we propose an extension of the SRIVC method that computes the filtered regressors exactly for a wide class of input signals whose intersample behaviour is known and prove its consistency for multisine input excitations.

The generalised equation error for the proposed approach is $$\label{gee2}
    \varepsilon(t_k) = A(p)y_f(t_k)-\{B(p)u_f(t)\}_{t_k},$$ where $u_f(t) = \frac{1}{A(p)}u(t)$. In , the predicted output measurement is explicitly calculated by first computing the underlying CT signal, and later evaluating it at $t=t_k$. The proposed estimator follows the procedure described in Algorithm \[algorithm1\], but the filtered regressor and instrument vectors in Equations and now become

&\_f(t\_k) = \^,&

and

&\_f(t\_k) = \^\_[t\_k]{}.&

Note that the $t_k$ in follows the notation in Remark \[remark1\].

**.** The proposed estimator is an extension of the standard SRIVC estimator that uses the complete CT input signal for identification. For input signals that are reconstructed exactly through a ZOH or FOH, this estimator is equivalent to the SRIVC estimator. Thus, the SRIVC-type estimator with prefiltering stage given by  and is generically consistent under the same assumptions as in [@pan2020consistency].

In order to further analyse the asymptotic properties of the proposed estimator, we first study its consistency for multisine inputs. Later, an extension 