# A Design Method for Gammachirp Filterbank for Loudness Compensation in Hearing Aids
## 4 Experiments and Discussion
### Loudness Compensation Experiment
#### 4.3.1 Objective Evaluation  
A new method to objectively evaluate speech quality was introduced to provide qualitative and quantitative analyses of processed speech. The speech intelligibility index, HASPI, and the speech quality index, HASQI, which represent system performance were calculated by using the function provided by the toolbox. It is worth noting that the input parameters include the vectors of the hearing loss in six audiometric frequencies, which can be acquired in the audiogram. That is, the result is related to the patient's hearing loss, and a series of objective experiments can be used instead of the subjective tests. The test audiograms were selected from the Occupational Hearing Loss (OHL) Surveillance Project of the NIOSH program for the Centers for Disease Control and Prevention in the United States. NIOSH is short for the National Institute for Occupational Safety and Health program, which collects worker audiograms across America [38]. In this work, we retrieved a dataset of 300 audiograms from participants, which were obtained using a standard pure tone audiometry protocol. Air conduction thresholds were measured at seven test frequencies: 500 Hz, 1000 Hz, 2000 Hz, 3000 Hz, 4000 Hz, 6000 Hz, and 8000 Hz. The hearing impairment can be divided into four grades: mild, moderate, severe, and profound according to the diagnostic criteria of the WHO [39]. Among the hearing-impaired patients corresponding to the 300 audiograms, 120 had moderate hearing loss, 100 had severe hearing loss, and 80 had profound hearing loss. The speech test signals used in the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**Number of Channels**} & \multicolumn{2}{c}{**Gammatone Filterbanks**} & \multicolumn{2}{c}{**Gammachirp Filterbanks**} \\ \hline \multicolumn{5}{c}{} \\  & & **Mean** & **Variance** & **Mean** & **Variance** \\ \hline \multirow{2}{*}{PESQ} & 8-channels & 3.7532 & 0.0117 & 4.0126 & 0.0118 \\  & 4-channels & 3.7233 & 0.0148 & 4.0742 & 0.0153 \\ \hline \multirow{2}{*}{STOI} & 8-channels & 0.9606 & \(3.4580\times 10^{-5}\) & 0.9701 & \(2.603\times 10^{-5}\) \\  & 4-channels & 0.9574 & \(5.3106\times 10^{-5}\) & 0.9604 & \(4.4718\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of speech quality indices. Figure 5: Speech quality index comparisons of 4-channel filterbanks. (a) Comparison of PESQ; (b) comparison of STOI. experiments were also from the CASIA Chinese emotional corpus. We randomly selected 50 speech test signals from the corpus. We conducted 300 rounds of loudness compensation experiments in this section according to the audiograms of 300 hearing-impaired patients. In the previous analysis, it can be seen that the 4-channel gammachirp filterbank had good fidelity. In this experiment, a 4-channel filterbank was used as an example. The filterbanks used in each round of experiments were combined according to a specific audiogram. For each audiogram, the main experimental steps were as follows. Based on the channel division method described above, a 4-channel gammachirp filterbank was first obtained. Then, the input speech test signal was passed through the filterbank, and the compensation gains were calculated with the FIG6 prescription formula. The FIG6 prescription formula is a prescription procedure that provides a set of rules to calculate the required gain under three input intensities (40, 65, and 90 dB SPL) according to the hearing threshold. This can be used to adjust the gain to the input signals, making speech intelligible and the overall loudness comfortable [27]. Lastly, the processed subsignals were combined into a reconstructed signal as the final output. According to the experimental results, there were six main useful groups of 4-channel gammachirp filterbanks which were combined from the 16-channel filterbanks according to the patients' audiograms.