An indirect interpolation method for Head-Related Transfer Function pole-zero models

Abstract

School of Electronic and Information Engineering, Dalian University of Technology, 116023 P.R. China(Received 22 February 2008, Accepted for publication 1 April 2008)Keywords: HRTF, Interpolation, Pole-zero model, All-zero modelPACS number: 43.60.Gk, 43.66.Qp [doi:10.1250/ast.29.329]1. IntroductionHead-related transfer function (HRTF), which describesthe path between the sound source and the ear, plays animportant role in 3D sound system [1]. The spatial perceptionusing headphone can be controlled by binaural synthesisthrough HRTF. However, the system has to store the HRTFsof all directions to realize natural spatial perception, since theHRTF varies as a function of the sound direction. In fact, it isimpossible to obtain the HRTFs of all directions throughmeasurements because of the enormous amounts of time andphysical loads of the listener. One solution to this problem isto obtain the HRTFs in arbitrary directions from a limitednumber of measured HRTFs.Some interpolation methods have been developed whichmainly focused on HRTF all-zero models, such as the linearinterpolation method [2], the inter-positional transfer function(IPTF) method [3], etc. But pole-zero model is more preferredin binaural synthesis because of its low computation andmemory cost. In [4], balanced model truncation method isemployed to reduce the order of HRTFs. In [5], the IIR filterof HRTF is designed taking the log-magnitude errors intoaccount. And in [6], the IIR filter is designed in warpedfrequency domain. Although pole-zero modeling of HRTF hasobtained great progress, interpolation methods that are bothautomatic and effective for pole-zero models have not beendeveloped so far. Generally, interpolation of pole-zero modelsmay be realized by convex combinations of pole (zero) valuesfrom the neighboring HRTF models [7]. As an improvementof the convex combination method [7], records the pole (zero)tracks during the iterated approximation, and incorporatesthem to increase the interpolation accuracy. But the improvedmethod in [7] is not applicable since extra information of thepole (zero) tracks has to be stored.In this paper, an indirect interpolation method for HRTFpole-zero models is developed based on the all-zero interpo-lation methods. First, the method transforms the pole-zeromodels to all-zero models. Then, the target HRTF is interpo-lated from the reference all-zero models using the linearinterpolation method. Last, the interpolated all-zero model istransformedbacktothepole-zeromodel.Theproposedmethodhas better interpolation accuracy than conventional methods,and does not need calculating the pole (zero) positions.2. The indirect interpolation methodSuppose two reference pole-zero models B