## 4 Experimental Results
### Measurements of the Frequency Discrimination  
Before processing frequency shifting, frequency resolution of the hearing-impaired person needs to be measured. Traditionally, [PERSON] proposed the psychophysical tuning curves (PTCs) method to obtain the frequency selectivity using a narrowband noise masker that sweeps in frequency [14; 15]. Rapid methods for PTCs measurement to improve the maneuverability, thereby saving measuring time and reducing complexity, have also been proposed [16; 17]. The Q\({}_{\rm 10 dB}\) calculated by the curve indirectly reflects the frequency resolution of the subject at a certain frequency [18; 19]. However, for sensorineural hearing-impaired patients, the measured Q\({}_{\rm 10 dB}\) will fail when the minimum  
Figure 4: Pure tone audiograms for the subjects: (**a**) S1; (**b**) S2; (**c**) S3; (**d**) S4; (**e**) S5; (**f**) S6. sound level is not recorded at which the patient is able to discriminate the probe signal from masker, or the bandwidth corresponding to 10 dB above the minimum level is wider than the measuring field. In our experiments, an alternative subjective listening test is conducted to obtain the frequency discrimination thresholds in different frequencies. Two pure tone signals (the probe signal and the offset signal) controlled and generated by computer software are emitted sequentially in a non-overlapping manner with 100 ms interval between them. The sound level is set to the most comfortable level (MCL) of the subject. Subjects are required to give indication when they are able to hear the two distinct sounds. According to the indication by the subject, the software adjusts the frequency offset until the subject reaches the discrimination threshold for which he/she is unable to identify [20]. The main steps of the proposed frequency discrimination measurement are as follows:  
1. The software plays an audio sequence at the testing frequency. The sequence consists of two 1-second pure tone signals with a 100 ms interval between them, namely \"pure tone 1--pause--pure tone 2\". In the sequence, pure tone 1 is the probe signal at the testing frequency, and pure tone 2 is the offset frequency signal or the same probe signal. 2. Each sequence is played once or twice. The second play is optional and activated by the listener. The listener needs to decide whether the two signals are identical. 3. The software adaptively adjusts the frequency offset according to the correctness of the subject's indication for the tone. The frequency offset values \(\Delta f\) can be set as \(\left[ \begin{array}{cccccc}\frac{1}{2}&\frac{1}{4}&\frac{1}{8}&\frac{1}{16} &\frac{1}{32}&\frac{1}{64}&\frac{1}{128}&\frac{1}{256}&\frac{1}{512}\end{array}  \right]\times f\), with initial frequency offset \(\Delta f=\frac{1}{2}f\), where \(f\) is the frequency of the probe pure tone. 4. When the subject gives N (N can be set by the software) times correct indications, then the frequency offset \(\Delta f\) is halved. When the subject hits N times incorrect indications, the frequency offset \(\Delta f\) is doubled. Otherwise the frequency offset is held constant and the testing continues. 5. When the offset is switched back and forth between the adjacent [\(\Delta f_{1}\)\(\Delta f_{2}\)]-M times, or the offset \(\Delta f_{2}\) is already tested M times, the frequency discrimination threshold at the probe frequency is considered to be the geometric average of the last two adjacent frequencies \(\left[ \begin{array}{cc}\Delta f_{1}&\Delta f_{2}\end{array} \right]\). The measurement moves to the next frequency and then returns to step 1. Coefficients of M and N can be set by the computer software to meet the application requirements, generally for 3-8 times. The larger the values of N and M, the more accurate the result will be, but at the expense of longer time consumption for the measurement. In our experiment, the values of N and M were set to 4 and 6, respectively.