## 4 Experiments and Discussion
### Validation of Proposed Noise Reduction Approach
#### 4.1.2 Experimental Results and Discussion  
We compared the noise reduction performance of the proposed approach to that of several conventional approaches, including spectral subtraction, adaptive comb filtering, and MMSE. First, we observed the spectrogram of the speech contaminated by the F16 fighter jet engine noise and de-noised speech by spectral subtraction and the proposed method. Figure 9 shows the result. As can be seen, two noise reduction approaches successfully eliminated the noise components. The proposed method demonstrated notable noise reduction performance in the overall time and frequency regions. In contrast, spectral subtraction did not perfectly reduce the noise components in the speech regions. Figure 9: Comparison of spectral figures according to noise reduction approaches: (**a**) original noisy speech; (**b**) de-noised speech by spectral subtraction; (**c**) de-noised speech by proposed approach. Several mathematical measurements, e.g., spectral distance (SD) and SNR, provide an efficient way to compare noise reduction performance. The SD calculates the distance between clean and de-noised speech in terms of spectral energy as follows:  
\[SD=\sqrt{\frac{1}{F}\sum_{\omega=1}^{F}\left[10\log_{10}\frac{X(\omega)^{2}}{ \hat{X}(\omega)^{2}}\right]^{2}}, \tag{12}\]  
where \(X(\omega)\) and \(\hat{X}(\omega)\) are the spectral energy of clean and de-noised speech in frequency bin \(\omega\), respectively. This measure calculates the SD for the overall spectral energy of \(F\) frequency bins for a given frame. If the noise components are eliminated perfectly, the distance between \(X(\omega)\) and \(\hat{X}(\omega)\) is very small. Thus, the SD value approaches 0. Figure 10 shows the noise reduction performance of each approach in terms of SD. As can be seen, the proposed MMSE approach achieved outstanding performance compared to the conventional approaches including the conventional MMSE. The proposed approach outperformed the conventional MMSE notably at severe noise levels (low SNR values) than higher SNR values, which indicates that the proposed hard-decision parameter correctly determines speech-present and speech-absent bins in severe noise environments. The conventional MMSE outperformed spectral subtraction and adaptive comb filtering, which demonstrates that the MMSE technique is very efficient at reducing non-stationary noises. The two approaches demonstrated different performances according to the SNR conditions. At low SNR values, spectral subtraction outperformed adaptive comb filtering, while an opposite tendency was observed at high SNR values. This result can be analyzed according to the property of adaptive comb filtering, which is highly dependent on the fundamental frequency extracted from the speech region. It is difficult to estimate the fundamental frequency correctly in severe noisy speech. Thus, filtering may induce adverse noise reduction under low SNR conditions. Next, we investigated noise reduction performance based on SNR. The SNR is a ratio of speech signals to noise signals contained in noisy speech signals. Thus, high SNR values are observed when fewer noise components are present. The SNR can be calculated directly from the input signals as follows:  
\[SNR=10\log_{10}\frac{\sum_{n=1}^{N}x(n)^{2}}{\sum_{n=1}^{N}\left(\hat{x}(n)-x(n )\right)^{2}}, \tag{13}\]  
where \(x(n)\) and \(\hat{x}(n)\) refer to clean speech and de-noised speech signals, respectively. This measurement calculates the ratio of clean speech signals to residual noise signals after noise reduction. If the noise signals are reduced perfectly, the difference between \(\hat{x}(n)\) and \(x(n)\) approaches 0, thereby increasing the SNR value. Figure 10: Comparison of noise reduction performance based on SD. Figure 11 shows the noise reduction performance of each method in terms of SNR. As can be seen, performance demonstrated a similar tendency to the SD results. The two MMSE approaches outperformed the other approaches. The proposed MMSE yielded the best performance.