## 4 Results and Discussion of the Nasal Cavity Three-Dimensional Structure Reconstruction System
### Results and Analysis of Nasal Acoustic Signal Preprocessing  
The first-stage incident wave and the first-stage reflected wave are separated from the original nasal acoustic signal to reconstruct the three-dimensional structure of the nasal cavity. The stable-state voltage value before the peak of the first-stage incident wave is selected as the DC offset component, corrected in the time domain. Subsequently, a Fourier transform is applied to the incident and reflected waves using 255 sample points at a sampling frequency of 100 kHz. The time-domain and frequency-domain plots of the input impulse responses from the straight tube model and the simulated nasal cavity model, both before and after the elimination of the DC offset component, are shown in Figure 11.  
Figure 10: (**a**) Original nasal acoustic signal of the straight tube model. (**b**) Original nasal acoustic signal of the simulated nasal model. Figure 9: (**a**) The straight tube model. (**b**) The simulated nasal cavity model. From Figure 11, it can be seen that the influence of the DC offset component on the input impulse response primarily appears as changes in amplitude. The reason for this phenomenon is that the DC offset component changes the amplitude of the incident and reflected waves at zero frequency in the frequency domain. This change subsequently modifies the baseline value of the DC component within the input impulse response. High-frequency noise also affects the input impulse response, which can be eliminated by introducing a constraint factor. Based on the step of eliminating the DC offset component, the time-domain and frequency-domain plots of the input impulse responses from the straight tube model and the simulated nasal cavity model, both before and after the introduction of the constraint factor, are shown in Figure 12.  
From Figure 12, it can be clearly seen that the constraint factor significantly weakens the amplified high-frequency noise during the computational process. Its effect is similar to that of the low-pass filter. The magnitude of the constraint factor determines the frequency band of the noise elimination. When the value of the constraint factor is too small, the high-frequency noise is not eliminated cleanly, resulting in an unsatisfactory denoising effect. This subsequently impacts the amplitude of the input impulse response in later calculations. This eventually leads to an inaccurate result for the final nasal cavity three-dimensional structural reconstruction. Conversely, if the constraint factor is excessively large, it weakens the amplitude of certain low- and medium-frequency bands, resulting in a smoother input impulse response curve. However, some of the low- and medium-frequency characteristics of the input impulse response will be lost. Based on the analysis of the results of several experiments, \(q=0.1\) is chosen for high-frequency denoising. In this setting, it effectively eliminates high-frequency noise from the input impulse response sequence while preserving the overall low- and medium-frequency features. Figure 11: (**a**) Partial input impulse response frequency spectrum of the straight tube model. (**b**) Input impulse response time sequence of the straight tube model. (**c**) Partial input impulse response frequency spectrum of the simulated nasal cavity model. (**d**) Input impulse response time sequences of the simulated nasal cavity model. Results and Analysis of the Nasal Cavity Three-Dimensional Structure Hierarchical Reconstruction Method  
The cross-sectional area values of different depths of the nasal cavity were obtained by analyzing the input impulse response sequences using a hierarchical reconstruction method. The standard curves of the two-dimensional depth-cross-sectional area curves were plotted using the actual physical size of the two tested models and compared with the reconstruction results of the original nasal acoustic signals using different preprocessing methods.