## 1 Introduction  
Currently, signal processing research in digital hearing aids is mainly focused on improving \"audibility\" of acoustic signals, which is typically attempted to achieve loudness compensation and dynamic range compression of input sound in different frequency and sound pressure levels. These methods essentially are aimed to achieve a certain intensity of output sound in the digital hearing aids which will fit the characteristics of hearing-impaired patients. It is known that hearing impairment affects auditory threshold, sound analysis ability, and temporal gap discrimination. Therefore, even when they are able to hear the sound, they may not understand the meanings [1]. This situation occurs particularly when the hearing-impaired patients lose the ability to analyze the sounds. In general, a cochlea in a normal ear is able to distinguish various frequency components in speech sounds by producing vibration in different locations within the cochlea. In contrast, an impaired cochlea is unable to properly differentiate frequencies, which leads to frequency confusion and the inability to understand the speech sounds [2; 3; 4; 5]. This situation is further exacerbated when the speech sounds are submerged in a noisy or disturbing environment [6]. In recent years, some acoustic signal processing algorithms have been proposed by researchers to improve the frequency resolution of hearing-impaired patients. A compression method was proposed by [PERSON] and [PERSON] [7], in which the input audio signal is divided into several sub-bands and then compressed to the center frequency within each band. Using this method, the frequency difference between the signal components is widened, and the aforementioned frequency confusion is alleviated. In previous studies [8; 9], the cause and effect of frequency resolution decrease has been considered. It has been shown that when the response curve of the cochlear filter is widened, the peak-valley difference of the spectrum is decreased, which makes it difficult to perceive the formants of the speech. The Spectral Contrast Enhancement (SCE) algorithm is proposed which enhances the spectrum of the original speech signal by increasing the amplitude difference while maintaining the original sound pressure level. Previous experimental results [8; 9] showed that a certain degree of improvement was provided by this method in speech recognition. There are also some prior works on improving audibleness for severely hearing-impaired patients [10]. These patients usually suffer from deafness or partial deafness because of severe loss of listening capability in the high frequency region. A frequency-lowering algorithm which moves high frequency components of the input audio signals into lower frequency regions was proposed in [10; 11]. By using this algorithm, the severely hearing-impaired persons can then perceive the previously lost high frequency components sounds as they have been shifted into a lower frequency range that is audible for the patients. However, high frequency hearing loss is only one of the symptoms of neurosensory deafness. There are other typical audiograms of neurosensory deafness, such as flat-shaped, slow descending-shaped, V-shaped (which is also called notched), island-shaped, and many others [12]. Different types of hearing loss usually have been faced with various difficulties in frequency resolution, for which the frequency-lowering algorithm is not able to accommodate. In a study by [PERSON] et al. [13], advantages of frequency compression in noisy environment are researched. Originating from the frequency lowering algorithm, a piecewise-linear frequency shifting algorithm for digital hearing aids is proposed to tackle deteriorated frequency resolution of V-shaped hearing loss patients. Different from the frequency lowering algorithm, which improves high frequency resolution only, the proposed algorithm has the ability to improve the frequency resolution of the patient in any frequency range.