# Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating
## 4 Experiments and Results Analysis  
We verified the nonlinearity of built-in accelerometer in the smart device by experiments. As shown in Figure 7, we placed two smartphones (one is the Motorola Nexus 6, another is the HUAWEI Honor 8) closely on the surface of a still wooden table. In order to obtain the voice excitation signal with stable intensity and frequency, the smart-phones received the voice signal from two loudspeakers which were fixed above at close distance. Then, the output signals of an accelerometer in the Motorola Nexus 6 were extracted. Simultaneously, the original voice from loudspeakers was recorded by HUAWEI Honor 8 as a comparison. As excitation signals, the three specific words \"on\", \"zero\" and \"two\" were spoken and played by loudspeakers. Each word was repeated 10 times with 3 seconds intervals between each repetition. Moreover, we repeated the experiment under a different distance between the speaker and mobile phone with 5 cm, 10 cm, 15 cm, 25 cm, and 30 cm, respectively.  
The output signals of the built-in accelerometer on X, Y and Z-axis at different distances from loudspeakers are shown in Figure 8. As a comparison, the output signals of the built-in microphone at different distances are shown in Figure 9. Besides, it is important to note that the gravity which is loaded on the Z-axis signal needs to be eliminated. It can be clearly found that the built-in accelerometer had obvious response output when we made voice as an excitation although with noise effect.  
Figure 8: _Cont._  
Figure 7: Experiment setup. (**a**) Experiment equipment; (**b**) Experiment setup.  
Figure 8: The output signal of the accelerometer at different distances. (**a**) The output signal of the accelerometer at distance of 5 cm; (**b**) The output signal of the accelerometer at distance of 10 cm; (**c**) The output signal of the accelerometer at distance of 15 cm.  
Figure 9: _Cont._  
Using the optimal delay time \(\tau\) and embedding dimension \(m\) which was determined by previous calculation, the reconstruction attractors with the condition of \(\tau{=}3,4,5,6\) for X, Y and Z-axis of the built-in accelerometer shown in Figures 10-12 are attractors.  
Figure 10: The attractors of \(\tau\) = 3,4,5,6 at X-axis when saying “oh”. (**a**) The attractor of \(\tau\) = 3; (**b**) The attractor of \(\tau\) = 4; (**c**) The attractor of \(\tau\) = 5; (**d**) The attractor of \(\tau\) = 6.  
Figure 9: The recorded voice at 5 cm and 30 cm, respectively for comparison. (**a**) The recorded voice at 5 cm; (**b**) The recorded voice at 30 cm.  
Figure 11: The attractors of \(\tau=3,4,5,6\) at Y-axis when saying “two”. **(a)** The attractor of \(\tau=3\); **(b)** The attractor of \(\tau=4\); **(c)** The attractor of \(\tau=5\); **(d)** The attractor of \(\tau=6\).  
Figure 12: The attractors of \(\tau=3,4,5,6\) at Z-axis when saying “zero”. **(a)** The attractor of \(\tau=3\); **(b)** The attractor of \(\tau=4\); **(c)** The attractor of \(\tau=5\); **(d)** The attractor of \(\tau=6\).  
It was clearly found from these figures that the convergence of attractors when \(\tau=3\), 4 and \(m=4\) are better than others, which is consistent with the calculation results in Section 3. However, the edges of these attractors were not smoothing due to the effect of white noise in original output signals which were generated by metal plate capacitance vibration inside the acceleration when it received voice signal.