# A Design Method for Gammachirp Filterbank for Loudness Compensation in Hearing Aids
###### Abstract  
Because the hearing impaired often experience different degrees of hearing loss along with the loss of frequencies, the loudness compensation algorithm in hearing aids decomposes the speech signal and compensates with different frequency bands based on their audiograms. However, the speech quality of the compensated signal is unsatisfactory because the traditional filterbanks fail to fully consider the characteristics of human hearing and personalized hearing loss. In this study, an effective design for the gammachirp filterbank for the loudness compensation algorithm was proposed to improve the speech quality of hearing aids. Firstly, a multichannel gammachirp filterbank was employed to decompose the signals. Then, the adjacent bands were merged into one channel, guided by the proposed combination method. After obtaining the personalized filterbank, each band conducted a loudness compensation to match the requirements of the audiograms. The excellent advantage of the gammachirp filterbank is that it can simulate the characteristics of the basilar membrane. Furthermore, the novel channel combination method considers the information from the audiograms and the relationship between frequency ranges and speech intelligibility. The experimental results showed that the proposed multichannel gammachirp filterbank achieves better speech signal decomposition and synthesis, and good performance can be gained with fewer channels. The loudness compensation algorithm based on the gammachirp filterbank effectively improves sentence intelligibility. The sentence recognition rate of the proposed method is higher than that of a system with a gammatone filterbank by approximately 13%. digital hearing aid; gammachirp filterbank; human auditory; loudness compensation; speech quality +
Footnote †: journal: Accepted: 1 February 2022  
and the filterbank in references [7; 8] was developed by employing interpolated, complementary linear-phase FIR filters and a frequency-response masking technique. Dividing the spectral into uniform bands is the most straightforward method, but does not consider the characteristics of human hearing and the differences between audiograms. Thus, nonuniform filterbanks that can adapt to the hearing characteristics and the matching requirements of different audiograms have recently attracted widespread attention from scholars [9; 10; 11]. The gammatone filterbank is one of the representative nonuniform filterbanks used in hearing aid applications that is able to simulate the auditory model of the cochlea of the human inner ear. It can also simulate the spectrum analysis functions, and the frequency selectivity of the human ear [12; 13]. However, the amplitude-frequency response curve of the gammatone filter is symmetrical at about the center frequency and the amplitude is independent of the intensity, which cannot reflect the asymmetry and intensity-related characteristics of the basilar membrane curve. Considering these drawbacks, some scholars have put forward a model of the gammachirp filter, developed on the basis of the gammatone filter in accordance with physiological and psychological experimental data. This filter retains the advantages of the gammatone filter, but also makes up for its defects in terms of asymmetry and intensity dependence [14]. In recent years, the gammachirp has made some achievements as an ideal auditory filter in speech signal processing, such as audio coding, formant estimation, speaker recognition, speech signal analysis, and simulation of the human ear basement membrane [15; 16; 17; 18; 19]. To address these challenges, this study proposes a novel method to apply the gammachirp filterbanks to decompose input signals. Furthermore, we propose a new channel-division method to satisfy different types of audiogram matching requirements. The key idea of the proposed method is to consider the relation between frequency ranges and speech intelligibility and the specific audiogram features.