## 4 Varying Noise Level--Speech Command Results
\[=\frac{d_{0}(55)f_{0}(55)+d_{1}(55)f_{1}(55)+d_{2}(55)f_{2}(55)+d_{3}(55)f_{3}(55)+ d_{4}(55)f_{4}(55)}{f_{0}(55)+f_{1}(55)+f_{2}(55)+f_{3}(55)+f_{4}(55)}. \tag{3}\]  
\[=\frac{0\cdot 0+1\cdot 0+2\cdot 23+3\cdot 0+4\cdot 0}{0+0+23+0+0}=2. \tag{4}\]  
When \(x=60\) dB  
\[y(60)=\frac{\sum_{i=0}^{4}d_{i}(60)f_{i}(60)}{\sum_{i=0}^{n}f_{i}(60)}. \tag{5}\]  
\[=\frac{d_{0}(60)f_{0}(60)+d_{1}(60)f_{1}(60)+d_{2}(60)f_{2}(60)+d_{3}(60)f_{3}( 60)+d_{4}(60)f_{4}(60)}{f_{0}(60)+f_{1}(60)+f_{2}(60)+f_{3}(60)+f_{4}(60)}. \tag{6}\]  
\[=\frac{0\cdot 1+1\cdot 4+2\cdot 30+3\cdot 0+4\cdot 0}{1+4+30+0+0}=1.8286. \tag{7}\]  
When \(x=65\) dB,  
\[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]0  
When \(x=70\) dB,  
\[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]1  
When \(x=75\) dB,  
\[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]2  
When \(x=80\) dB,  
\[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]3  
When \(x=85\) dB,  
\[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]4  
Similarly, the frequency map and trendline of the other 11 speech command phrases are presented in Figures 4-6, after performing a similar analysis. Figure 4 shows the results of four speech commands. In particular, Figure 4a,b shows the frequency map and trendline of the second speech command (SC2), \"Go Backward\". This is a two-word command which seems to have a slightly better performance across the experiment participants than the first speech command (SC1), \"Go Forward\", particularly between 70 dB and 80 dB. Figure 4c,d shows the frequency map and trendline of the third speech command (SC3), \"Step Left\", another two-word command. Figure 4e,f shows the frequency map and trendline of the fourth speech command (SC4), \"Step Right\", a two-word command which seems to have been the most successful of all the other two-word commands previously presented. SC4 has a recognition accuracy of over 90% at 75 dB and about 70% at 80 dB. Figure 4g,h shows the frequency map and trendline of the fifth speech command (SC5), \"Hover\", a one-word command, which had the poorest performance of all the speech command set in the experiment. It performance was observed to be as low as 22% at 65 dB. This was mainly attributed to its subtle articulation, which leaves it easily prone to noise corruption even at low noise levels. In addition, the SC5 failure was also partly attributed to the speech ASR implementation not being robust enough. Commercial or industrial speech ASR interfaces, such as the Amazon Echo, Apple Siri, and Microsoft Cortana, may offer an improved performance due to their use of more advanced and online AI learning algorithms, whereas the custom CMU Sphinc ASR that was used in this application was based on offline hidden Markov models (HMM). \[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]5 Frequency map and trendlines I. (**a**) SC2 frequency map, (**b**) SC2 trendline, (**c**) SC3 frequency map, (**d**) SC3 trendline, (**e**) SC4 frequency map, (**f**) SC4 trendline, (**g**) SC5 frequency map, (**h**) SC5 trendline. \[y(x)=\frac{\sum_{i=0}^{n}d_{i}(x)f_{i}(x)}{\sum_{i=0}^{n}f_{i}(x)}, \tag{1}\]6 Frequency map and trendlines II. (**a**) SC6 frequency map, (**b**) SC6 trendline, (**c**) SC7 frequency map, (**d**) SC7 trendline, (**e**) SC8 frequency map, (**f**) SC8 trendline, (**g**) SC9 frequency map, (**h**) SC9 trendline. Figure 5 shows the results of four more speech commands, SC6-SC9. Figure 5a,b shows the frequency map and trendline of the sixth speech command (SC6), \"Land\", which is also a one-word speech command. However, unlike SC5: Hover, SC6: Land, had a better performance, with recognition accuracy of over 90% at 75 dB and about 67% at 80 dB. Figure 5c,d shows the frequency map and trendline for the seventh speech command (SC7), \"Go Forward Half Metre\", which is a four-word command.