## 1 Introduction
The reason for choosing 10 nm as the new standard is owing to the improvements in measurement capabilities achieved by the European Union's Horizon 2020 research and innovation program. This funded three projects to explore the possibility of passing from an SPN23 to an SPN10 standard, with d50 = 10 nm and d90 = 23 nm [34]. These projects are DownToTen, PEMs4 Nano, and SUREAL-23 [34]. The former two focused on developing a new PEMS (portable emissions measurement system) to quantify particle numbers (PNs) of current and future vehicle technologies for both laboratory and RDE (real driving emissions). On the other hand, the latter concentrated its efforts on producing new technologies to solve exhaust sampling and treatment methodology issues [34]. All of these contributed to attaining d50 = 10 nm for the new SPN10 regulation. An alternative method to find TPN or SPN is by using a DMS (differential mobility spectrometer). One of the most common commercially available DMS machines used in research is Combustion DMS500. Generally, this is mainly utilised to find PSD (particle size distribution), but with the use of empirical approximations based on instrument calibrations, the particle count from DMS500 can be obtained [35]. One method to convert PSD to PMP-comparable was with lognormal fitting [35; 36]. This was effective for the SPN23 standard with d50 = 23 nm and d90 = 41 nm. However, for the implementation of the newly discussed SPN10, where sub-23 nm particles are observed, lognormal fitting is no longer viable due to fitting modes being close to prescribed size limits, substantially decreasing its reliability [35; 36]. Another way to obtain the PMP equivalent TPN from the DMS is to use digital filtering (DF) [35; 36; 37]. The equation below (where dp is the particle diameter) was proposed by [PERSON] [35] and employed in some studies [38; 39], showing results representative of the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Regulation** & **Nitrogen Oudes (NOx)** & **Particulate Number (PN)** & **Particulate Mass (PM)** & **Carbon Monoxide (CO)** & \begin{tabular}{c} **Non-Methane Organic** \\ **Gases (NMOGs)** \\ \end{tabular} \\ \hline Euro 6 (Current) & 80 mg/km & \begin{tabular}{c} 6 \(\times\) 10\({}^{11}\)/km including all \\ \textgreater{}23 nm particles (SPN23) \\ \end{tabular} & 4.5 mg/km & 1000 mg/km & 68 mg/km \\ \hline Euro 7 (CLOVE) & 20 mg/km & \
\begin{tabular}{c} 1 \(\times\) 10\({}^{11}\)/km including all \\ \textgreater{}10 nm particles (SPN10) \\ \end{tabular} & 2 mg/km & 400 mg/km & 25 mg/km \\ \hline Euro 7 (European &
\begin{tabular}{c} 6 \(\times\) 10\({}^{11}\)/km including all \\ \textgreater{}10 nm particles (SPN10) \\ \end{tabular} & 4.5 mg/km & 500 mg/km & 68 mg/km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Euro 7 CLOVE proposition (adapted from [13]). SPN23 standard. As DMS has a higher particle size resolution than the condensation particle counter (CPC), capturing particles down to 5 nm, digital filtering works by prescribing the SPN23 detection efficiencies with the filter [35] and suppressing the high-level noise for sub-23 nm particles. A Wiebe function structure was adopted for the filtering operation [35; 36]. \[f\big{(}d_{p}\big{)}=\left\{ \begin{array}{c}1-exp\left[-3.54\left(\frac{d_{p }-14}{40}\right)^{1.09}\right],\ d\geq 14\\ 0,\ d<14\end{array} \right\} \tag{1}\]  
This was validated in [35], where results from DMS500 Wiebe were compared to AVL CPC (called APC) with SPN23 detection efficiencies. Therefore, this equation can be applied to prescribe CPC detection efficiency of d50 = 23 nm and d90 = 41 nm on DMS500 PSD data. Two more digital filters were proposed by [PERSON] et al. [40] and one by [PERSON] et al. [36] to model counting efficiencies that have been proposed for future SPN10 regulations. However, these would need to be validated against a CPC with the same detection efficiency as it was done for Equation (1). [PERSON] et al. 's [36] equation to prescribe detection efficiency of d65 = 10 nm and d90 = 15 nm is reported here in Equation (2).