For this procedure, only regular sampling is considered, although extensions to irregular sampling are also possible.

The proposed algorithm for computing $\varphi_f(t_k)$ and $\hat{\varphi}_f(t_k)$ at the $j$-th iteration of the SRIVC-type method goes as follows:

1.  Given the sampling period $h$ of $y(t)$, (over)sample $u(t)$ with sampling period $\delta h$, where $\delta\ll 1$.

2.  From $\theta_j$, form the prefilters of interest, namely $p^i/A_j(p)$ and $B_j(p)p^l/A_j^2(p)$ for $i=0,\dots,m$; $l=1,\dots,n$.

3.  Compute the Delta equivalent [@middleton1990digital] of the prefilters, and calculate the response at instants $t_k$ of each filter to the fast-sampled version of $u(t)$ in the Delta domain.

The Delta domain description leads to an exact simulation of the underlying CT system when $\delta h\to 0$. Thus, the SRIVC-type method with prefilters computed as in steps 1, 2 and 3 above calculates the filtered regressor and instrument vectors accurately if the oversampling period $\delta h$ is chosen small as compared to the sampling period. Due to potentially high sampling rates, the use of the Delta operator is needed for ameliorating rounding errors and ill-conditioning problems regarding the sensitivity of the coefficients of the prefilters. Note that step 3 of the algorithm can be easily performed by using the Delta domain Toolbox 