## 4 Experimental Results
### The Performance of the Frequency Shifting Algorithm  
In order to verify the effect of the proposed frequency shifting algorithm on the six subjects with V-shaped audigrams, subject evaluation tasks for speech discrimination score (SDS) and speech \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** \\ \hline probe frequency/Hz & 4000 & 3000 & 4000 & 6000 & 4000 & 3000 \\ frequency discrimination threshold & \(\pm\)1.6\% & \(\pm\)3.2\% & \(\pm\)3.2\% & \(\pm\)6.3\% & \(\pm\)6.3\% & \(\pm\)1.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of six subjects at the frequencies of the highest hearing thresholds. -reception threshold (SRT) were performed. Speech discrimination score is the percentage of the speech words that a subject identifies correctly. The speech pressure level of 50% recognition score is defined as the speech reception threshold. For the choice of corpus, monosyllabic vocabulary, disyllabic vocabulary, and sentences were selected. Since a syllable is the smallest unit of Chinese language, monosyllabic lists are usually chosen for speech discrimination score tests. However, monosyllabic words cannot express complete semantics, coarticulation, allophone, and other phenomena in the language, so disyllabic spondaic words are commonly used for additional speech audiometry. The materials of the experiment were selected from the monosyllabic vocabulary and the disyllabic vocabulary in the Chinese Mandarin Speech Audiometry CD published by People's Medical Publishing House. The corpus meets the national standard GB/T15508 with reference to \"Acoustics Manual\" for word selecting and recording. The audiometry procedure was performed according to references [21; 22], and the software platform was established according to reference [23]. In the experiment, the materials were processed by the piecewise-linear frequency shifting algorithm. The range of frequency stretching was decided according to the results obtained from the frequency discrimination test and the value of stretching ratio \(\gamma\) was determined by Equation (1). The range of frequency compressing, the compressing ratios \(\beta_{1}\) and \(\beta_{2}\) were determined by Equations (2)-(3). In order to control distortion of the output signal, the value of the stretching ratio \(\gamma\) was set between 2 to 5, and the values of \(\beta_{1}\) and \(\beta_{2}\) were set between 0.9 to 1. Table 3 shows the stretching ratios and the compressing ratios of the six subjects. As shown in Figure 1, \(f_{a}\) and \(f_{d}\) can be set freely according to the channel edge frequencies. In this paper, we used \(f_{a}=0\) and \(f_{d}=8000\) Hz in all experiments to avoid the influence of the different channel widths. The original sample rate of the vocabularies was 44.1 kHz. This sampling rate was first changed to 16 kHz before processing. The frame length was 1024 samples with 512 samples overlapped. Figure 5 shows the spectrograms of the Chinese disyllabic word \"Xuduo\" (the meaning is \"many\") before and after the proposed algorithm. Here, \(f_{0}=4000\) Hz and the frequency stretching range was \(\left[3750\,\mathrm{Hz}\quad 4250\,\mathrm{Hz}\right]\) with the coefficients \(\gamma=2\), \(\beta_{1}=0.93\), and \(\beta_{2}=0.93\). Figure 5: Spectrograms of a Chinese disyllabic word. (**a**) Spectrogram before process; (**b**) Spectrogram after process.