utilizes interaural time difference (ITD) and interaural intensity difference (IID) to interpret the cause of spatial hearing. By virtue of these results, there have been some tentative applications in auditory display of multimedia systems, for instance, VoiceNotes of MIT Media Lab. However, there are still no fully successful models capable of explaining some of the phenomena associated with spatial hearing, such as the perception of a sound's position at an elevation, the "cone of confusion" and so on.In the ensuing research, people take cognizance of the cues implied in grotesque while a little inerratic spectrum. Thus, the systemic description of the entire relevant information, head-related transfer function (HRTF), has been introduced to depict them, where ITD can be seen as the delay between two ears and IID as the difference of HRTFs' magnitude. Moreover, people have constructed different mathematical models to simulate this delicate function, and tried to give a felicitous interpretation for this fancy phenomenon [1−4]. As a popular model structure, the principal component analysis (PCA) model has been greatly studied in this field [2−4]. Basically, researchers in Ref.[2] applied PCA to logarithmic magnitudes of HRTFs that were measured for 10 subjects and at 256 positions. In the PCA model, HRTFs for each position were represented as a weighted combination of a set of basis functions in a low-dimensional subspace, which were obtained from the measured logarithmic magnitudes of HRTFs. While the phase was approximated from the magnitude related to a certain position based on minimum phase characteristics. The spatial feature extraction and regularization model put forward in Ref.[3] contains the phase information during the HRTFs' reduction representation. Furthermore, a thin-plate spline using regulation procedures was also introduced to obtain a mathematical representation for sampled spatial positions. As a result, unmeasured positions' HRTFs can be approximately reestablished from the mathematical equation, which effectively surmount the spatially discrete limitation of HRTFs' measurement. However, both these PCA models were used to process complex valued (amplitude and phase) head-related transfer functions, and needed a lot of complex and logarithmic operations. In Ref.[4], Wu applied Karhunen-Loève transformation to HRIRs in time Abstract In the research on spatial hearing and realization of virtual auditory space, it is important to effectively model the head-related transfer functions (HRTFs) or head-related impulse responses (HRIRs). In our study, we managed to carry out adaptive non-linear approximation in the field of wavelet transformation. The results show that the HRIRs' adaptive non-linear approximation model is a more effective data reduction model, is faster, and is 5 dB on average better than the traditional principal component analysis (PCA) (Karhunen-Loève transform) model based on relative mean square error (MSE) criterion. Furthermore, we also discussed the best bases' choice for t...