## 5 Results and Discussion  
To examine the accuracy of the developed DAQ system, the \(S_{2f/1f}\) was measured for a transmitted signal with a known water vapour mole fraction of 3%. The SNR of the transmitted signal was 56 dB [17]. The measured \(S_{2f/1f}\) spectrum was compared with that obtained by digitising and demodulating the transmitted signal using MATLAB (i.e., ideal signal, with no noise and full bit resolution). For the same transmitted signal, the \(S_{2f/1f}\) spectrum was also obtained for the two state-of-the-art approaches identified in Section 1: (a) using an offline raw data processing approach, and (b) using the standard I-Q demodulation method. Figure 7 shows a comparison of the results of the average of 20 measurements. In the offline processing approach, the DAQ samples the raw transmitted samples, and demodulation is completely done on the high-level processor, while in the standard I-Q method, four pre-processed components are sent to the high-level processing. For each of these methods, the \(S_{2f/1f}\) spectrum was also compared with the ideal spectrum. As discussed earlier, the peak of the \(S_{2f/1f}\) signal is proportional to the gas concentration. Hence, we first evaluated the performance of each of the signals around the peak of the \(S_{2f/1f}\) spectrum. Figure 6: DAQ set-up for WMS. The AWG contains signals generated from realistic absorption data from the HITRAN database. The generated signals are digitised, processed to extract harmonics of interest, and transmitted to a high-level processor. As shown in the figure, the offline processing technique achieved the most accurate result around the peak point, with an error of 0.17%, while the standard I-Q method had an error of 2.53%. Our proposed technique had an error of 0.34%, which demonstrated the superior performance of the proposed technique over the standard I-Q method. The superior accuracy of the proposed technique is enabled by the additional on-chip processing, which minimises the amount of data to be transferred to the high-level processor. It is worth noting that although the offline technique had a superior noise performance (Figure 7a), it had a very high bandwidth requirement. We quantified the bandwidth requirement for the three DAQ sensing architectures with the parameters above, i.e., sampling rate of 15.625 MSps, modulation frequency of 125 kHz, and a laser scan rate of 125 Hz. The required bandwidth is shown in Table 3. As is shown, for the real-time operation, the offline processing architecture had a bandwidth of 250 mega bits per second (Mbps), with the proposed technique requiring only 3 Mbps, only 1.2% of the bandwidth of the raw sample technique, an improvement of 98.8%. Furthermore, compared to the standard I-Q technique, an improvement of 25% in bandwidth is achieved. Therefore, for bandwidth constrained applications, the proposed technique will be a better choice. \begin{table}
\begin{tabular}{c c c} \hline \hline
**DAQ Architecture** & **Bandwidth (Mbps)** & **\% Improvements** \\ \hline Offline (raw data sampled real time) & 250 & - \\ Standard I-Q 1 [6; 17] & 4 & - \\ Proposed 1  & 3 & 25 (98.8) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Bandwidth requirement of DAQ architectures. Figure 7: Comparison of accuracy of the proposed DAQ system with conventional techniques. In (**a**), raw transmitted samples were demodulated offline on a high-level processor. In (**b**,**c**), the standard I-Q demodulated technique and the proposed DAQ system operated in real time for a fixed bandwidth. However, it is worth noting that for multiple species detection using frequency multiplexing (e.g., in [16]), the bandwidth requirements for both the standard I-Q and the proposed architecture doubles for each additional frequency. In this case, further analysis is needed to ascertain the bandwidth and accuracy improvements. Nevertheless, for single species detection using WMS or for multiple detection using time division multiplexing, the bandwidth and accuracy discussion above holds.