Fluid Dynamics and Acoustics Group


  Numerical Modelling (1997-2001)



Most current spatial sound reproduction systems are based on the concept of the binaural technology. These systems are referred to in the literature as ‘3D audio’ (Begault, 1994), virtual auditory display (Wenzel et al, 1993), virtual auditory space (Carlile, 1996), virtual acoustic imaging (Nelson et al, 1997), and similar variations. The goal of the system designer is to ensure that the reproduced signals in the ears of a listener, through either headphones or loudspeakers, are equivalent to those detected under real listening conditions. In order to manipulate the signals arriving in the eardrum of the listener in a binaural synthesis process, it is required to know the directional characteristics of the physically filtered signals, encoded in the Head-Related Transfer Function.

It should be noted that there are other approaches to produce spatial sound, which are not based on the HRTF. For example, ‘wave filed synthesis’ (Berkhout et al, 1993) reconstructs the propagating waves in a restricted area using the exact Helmholtz-Kirchoff equation, or ‘loudspeakers-walls’ system (Ono et al, 1998) which recreates an approximation of a desired impulse response of a room. Both methods require large number of loudspeakers. 

In recent years the number of scientific papers, products and applications associated with the HRTF has grown rapidly due to two main reasons (1) the advances in computing power and the possibilities to implement digital filters with low-cost DSP chips, and (2) advances in research on the physical, physiological, and psychoacoustical aspects of spatial hearing and the interaction between them.


High resolution mesh of the YK head (half model)

Scattered sound field - 1 KHz
One of the main limitations of the binaural technology is the generalisation of the HRTF of a particular listener or an artificial head for the entire population. When individualised HRTFs are used (i.e. either the recording is done with microphones positioned in the ears of the listener, or monophonic signals are synthesised with the listener’s HRTF) and we assume no errors are introduced in any part of the reproduction chain (transducers, acoustic medium, head movements, etc…) we may not need to deal with the complexity of the perception of sound by the auditory system. In practice, errors are inevitable, and exact reproduction cannot be achieved. Therefore, psychoacoustical studies must be carried out in order to investigate the physical cues encoded in the HRTF and the perceptual importance of these in the auditory system.

It appears in many psychoacoustical studies published in the last 50 years that the task of localisation of sound is more complex than assumed originally in Lord Rayleigh’s duplex theory (Rayleigh, 1907). Although the significance of the external ear is now well recognised as a complex acoustical antenna, it is still not understood how the different cues are combined in the auditory system, and from the neurophysiological view if all the information detected by the pinna can be encoded by the nervous system.

High fidelity HRTFs are currently required by both the research community and the designers of virtual auditory displays. Traditionally, these databases are acquired by measurements. The procedure of measuring HRTFs is very time consuming, and expensive. These are currently limited to well-equipped acoustic laboratories only, and as a result, most HRTFs are either confidential or restricted to research purposes. There are also many problems encountered when these functions are measured, analysed and compared between different studies. For example it is difficult to define the point at which the microphone should be positioned in the ear canal, the type of transducers used, equalisation techniques, dealing with signal to noise ratio problems, etc. In addition, HRTFs are generally measured only at discrete points with a low directional resolution. As a result, any real-time virtual auditory display would need to make use of interpolated functions.


In this study, we suggest an alternative approach to acquire individualised HRTFs, by using computer simulation techniques rather than measurements. The conversion of imagery data into its acoustical response should be achieved, in principle, by solving the wave equation. The idea is not new, as this was stated by Weinrich (1984) who first investigated the response of the human head (without pinnae) using numerical techniques:

"The rather complicated geometric shape of the pinna makes a rigorous mathematical treatment very difficult – perhaps impossible"

 And recently also by Shinn-Cunningham and Kulkarni (1996):

“Theoretically, it is possible to specify the pressure at the eardrum for a source from any location simply by solving the wave equation…. Needless to say, this is analytically and computationally an intractable problem”

In this research, we attempt to investigate the feasibility of obtaining accurate HRTFs using computer simulation, and to develop a tool that can be used to investigate the acoustical characteristics of the external ear.


3D HRTF representation at 4 kHz using the principle of reciprocity

A mode shape of the external ear (DB60 pinna)

The focal point of this work is to investigate whether it is viable to predict high frequency components in the frequency response of the external ear using simulation tools. The targets and questions asked throughout the research are given below:

  • Investigate the feasibility of using various numerical techniques to investigate HRTFs at low to medium frequencies using simple models. Can we simulate the response of these simple models so that these can be used, for example, in a structural model, such as the one proposed by Genuit (1986, 1987)?

  • Simulate HRTF of accurate geometry models. Can we validate the results with measurements carried out in an anechoic chamber?

  • Develop a tool to investigate the acoustical characteristics of the human ear. Can we reduce our problem by substitution of the head with an infinite baffle, and concentrate on the contribution alone, independently of the other parts of the human body?

  • Identify common characteristics of the external ear by visualising the response at high spatial resolution at different azimuthal and elevation planes. By simulating and measuring a few pinnae under exactly the same controlled conditions, continuous maps of the variation of peaks and notches in the frequency response can be obtained. Are these results comparable with those found in the literature?

  • Investigate the frequency response of the external ear that can be used mathematically to reconstruct individualised HRTFs. In the area of HRTF modelling, low-order parametric functions are required mainly for the implementation of real time virtual auditory displays. Can we find, using simulation tools, common physical patterns that can be used for this purpose?

  • Validate the normal mode shapes measured by E.A.G Shaw and published over a period of three decades. To the author's best knowledge, his work summarising the mode shapes of the pinna has not yet been validated nor continued. Can we obtain the same patterns with our simulated pinnae models?

  • Visualise sound fields of virtual acoustic imaging systems using loudspeakers. The equalisation zone ('sweet spot') is primarily affected by the loudspeaker arrangement. Can we predict the sound field around the head, while designing an ideal cross-talk cancellation network with the individualised HRTFs modelled in the first step?