# Perceptual Characteristics of Voice Identification in Noisy Environments
## 2 Perceptual Characteristics in Different Noisy Environments
### Data Analysis and Results of Experiment 1  
After the data were processed, the accuracy of perceiving voice identity was calculated in conditions with white, pink, and speech noise. The result is shown in Figure 3 through fitted curves.  
It is shown that the influence of the three types of noise on the accuracy has a similar trend. The accuracy has a logarithmic increase with the increasing the SNR for all three curves. The accuracy perceived in speech noise is the lowest, while the accuracy perceived in white noise is the highest. The difference between the perception results under the three types of noise gradually weakens when the SNR increases. In order to compare the impact of noise types on the accuracy, a significance analysis was conducted on the perceptual data under three noise interference environments. The results showed that when the SNR was not less than 0 dB, there was no significant difference between the degrees of accuracy under different types of noise (\(p\) = 0.370). When the SNR was less than 0 dB, there were significant differences between speech noise and pink noise (\(p\) = 0.001) and speech noise  
Figure 3: Voice identity perception in different noise environments.  
and white noise (\(p=0.000\)), while the differences between pink noise and white noise were not significant (\(p=0.236\)).  
According to the above results, the perception data in noise environments are divided into three parts: the first type constitutes the data perceived in the speech noise environment with low (<0 dB) SNR; the second type is the average value of data perceived in pink and white noise environments with low (<0 dB) SNR; and the third type is the average value of data perceived in pink noise, speech noise, and white noise environments with high (\(\geq\)0 dB) SNR. In order to study the perceptual characteristics of voice identity in noisy environments, the above three types of perceptual data were fitted using the least squares-fitting method. The fitting formulas are shown in Equations (1)-(3)  
\[ACC_{L-S}=0.809+0.042\times\ln(\text{SNR}+9),\ R^{2}=0.96 \tag{1}\]  
\[ACC_{L-WP}=0.893+0.018\times\ln(\text{SNR}+9),\ R^{2}=0.90 \tag{2}\]  
\[ACC_{H}=0.899+0.019\times\ln(\text{SNR}+9),\ R^{2}=0.78 \tag{3}\]  
where \(ACC_{L-S}\) represents the accuracy perceived in the low SNR(<0 dB) speech noise environment, \(ACC_{L-WP}\) represents the accuracy perceived in the low SNR(<0 dB) white and pink noise environment, \(ACC_{H}\) is the accuracy perceived in the high SNR (\(\geq\)0 dB) noise environment, and R\({}^{2}\) is the fitting precision. Equations (1)-(3) are mathematical models that may be used to calculate the accuracy of voice identification, which is only perceived in noisy environments, and they have a greater level of accuracy with an R\({}^{2}\) greater than 0.75.  
To intuitively inspect the precision of the prediction models, a scatter diagram of the measured and predicted scores of voice identification is provided in Figure 4. It shows that each data set is distributed around the central line. This means that the precision of the mathematical models is high with respect to predicting perceptional accuracy in noise interference environments. The result of voice identity perception with only noise interference can be predicted directly by fitting Formulas (1)-(3).