**2. Head-Related Transfer Function**

The HRTF is a representation of the influence of the acoustic system formed by the pinna, head and human torso on the deformation of the acoustic signal spectrum reaching the listener's ear. The head's shape and tissue structure have a bearing on acoustic signal spectrum distortion (Batteau, 1967; Blauert, 1997; Hartmann, 1999; Moore, 1997). The changes in the spectrum enable the listener is able to more accurately localize the sound source in the space which surrounds her/him. In case of headphone listening the influence of the acoustic system formed by the pinna, head and human torso is eliminated and the acoustic signal received by the listener is unnatural – the listener localizes the sound source inside her/his head. Through the use of HRTF measurement results the signal can be so deformed that the listener subjectively identifies the spatial properties of the sound whereby the location of the sound source in the space surrounding the listener is

System for High Speed Measurement of Head-Related Transfer Function 3

measurement point and then these values can be applied while processing the results of the

, , *f S f Cf HRTFL R*

*H f HRTF f Sf Cf*

arg , , arg , , arg arg *HRTFL R*, ,

*HRTF f HRTF f j HRTF f L R*,, ,

 

, , , , *L R*

 *f HL R* 

 <sup>1</sup> , , , , , , *HRIR t HRTF t L R*

*L R*

It has been empirically proven that HRTFs are minimum-phase, therefore minimum-phase FIR filters are used to simplify the HRTF description interrelated (Cheng & Wakefield, 2001). Firstly, minimum-phase requirement allows to explicitly define the phase on the basis of the amplitude response. This is a consequence of the fact that the logarithm of the amplitude response and phase response in a casual system are related by the Hilbert transform. Secondly, the minimum-phase requirement allows to isolate the information about the ITD from the FIR characteristic describing the HRTF. When the minimum-phase filter has the minimum group-delay property and the minimum energy delay, most of the energy is accumulated at the beginning of the impulse response and the appropriate for the

In order to achieve the characteristic of the hearing impression related to a particular point in space there are three values to be measured: the left ear amplitude response, right ear amplitude response, and ITD. The characteristics of the filter include both the ITD and ILD information: time differences are included in the phase characteristic of the filter, whereas the level differences correspond with the total power of the signal transmitted through the filter interrelated (Cheng & Wakefield, 2001). The interaural time difference can be calculated by many various measurement methods: as a result of measurement with the participation of people, a result of the dummy-head measurement, simulations performed on the spherical and elliptical models, calculation based on Woodsworth-Slosberg formula

Conducting the measurements for a big number of people is a complicated issue (Møller et al., 1995; Møller et al., 1992). The head-related transmittance functions show a great individual variability: the discrepancy between the measurement results reaches about 3 dB

,

, , exp arg , , *L R*

 

   

, (3)

*f S f C f* , (4)

 , (5)

*F* , (6)

, ,*f* . (2)

*HL R*, ,

Further the HRTF value is calculated according to the following interrelations:

 

,

*L R*

Formula (1) can be also written in the frequency domain:

 

 

left and right ears minimum-phase HRTFs have zero delay.

, , *L R*

 

 

where: <sup>1</sup> *F* – inverse Fourier transform.

(Minnaar et al., 2000; Weinrich, 1992).

measurement.

and the HRIR value:

reproduced (Hartmann & Wittenberg, 1996; Horbach et al., 1999; Hen et al., 2008, Plaskota & Kin, 2002; Plaskota et al. 2003). Since there are many sound source locations in the space surrounding the listener many HRTFs are needed to accurately reproduce the location of the sound source in this space.

The function describing the direction-dependent acoustic filtering of sounds in a free field by the head, torso and pinna is called HRTF. Although it is obvious that the linear dependence between Interaural Time Difference (ITD), Interaural Level Difference (ILD) and the perceived location in space needs to be predicted, it is less obvious how the spectral structure and the location in space can be mathematically interrelated (Cheng & Wakefield, 2001). The first step towards understanding the significance of the signal spectrum in directional hearing was an attempt at physical modeling and empirical measurement followed by computer simulations of the ear's frequency response depending on the direction. The measured frequency response of the ear is subject to further analysis.

Formally a single HRTF function is defined as an individual right and left ear frequency response measured in a given point of the middle ear canal. The measurement is conducted in a far-field of the source placed in a free-field. Typical HRTFs are measured for both ears in a particular distance from the head of the listener for several different points in space. Thus the transmittance function related to the head depends on the azimuth angle, elevation angle and the frequency, and apart from that it has a different value for the left ear (L) and for the right one (R): *HRTFL R*, , , *f* . The HRTF's time-domain equivalent is the Head-Related Impulse Response (HRIR).

In fact a measured transmittance function includes also a certain constant factor. This factor characterizes the measurement conditions – the measurement chamber characteristic and the measurement path. This is a reference characteristic, and the value of this parameter is determined by measuring the impulse response without the presence of the measured subject. Therefore by additionally taking into consideration the reference characteristic the result of the transmittance function can be presented as

$$\mathcal{H}\_{\mathcal{L},\mathcal{R}}\left(\theta,\phi,t\right) = s\left(t\right) \* c\left(t\right) \* \mathcal{H}\mathcal{R}\mathcal{R}\_{\mathcal{L},\mathcal{R}}\left(\theta,\phi,t\right),\tag{1}$$

where: , , , *L R h t* – impulse response by the entrance to the ear canal,

*s t* – measurement signal,

*c t* – impulse response of the measurement system,

*HRIR t L R*, , , – impulse response related to the head.

In some conditions it can be assumed that *c t* is constant and not influenced by the measurement point's position in space. Then the *c t* value is a mean measurement result for several different azimuth angles and elevation angles. But if the measurement chamber does not fulfill the conditions of the anechoic chamber or in the room are present some elements which cause generating undesirable reflections, the *c t* factor is influenced not only by the time, but also by the position of the measurement point in the space surrounding the listener, and it differs for the left and right ear: *c t L R*, , , . In order to increase the accuracy of the measurement the *c t L R*, , , value can be measured for every measurement point and then these values can be applied while processing the results of the measurement.

Formula (1) can be also written in the frequency domain:

$$H\_{L,R}\left(\theta\_{\prime}\phi\_{\prime}f\right) = \mathcal{S}\left(f\right)\mathcal{C}\left(f\right)HRTF\_{L,R}\left(\theta\_{\prime}\phi\_{\prime}f\right). \tag{2}$$

Further the HRTF value is calculated according to the following interrelations:

$$\left| \text{HRTF}\_{L,R} \left( \theta, \phi, f \right) \right| = \frac{\left| H\_{L,R} \left( \theta, \phi, f \right) \right|}{\left| S(f) \right| \left| C(f) \right|}, \tag{3}$$

$$\arg\text{HRTF}\_{\text{L,R}}\left(\theta,\phi,f\right) = \arg H\_{\text{L,R}}\left(\theta,\phi,f\right) - \arg\text{S}\left(f\right) - \arg\text{C}\left(f\right),\tag{4}$$

$$\left| \text{HRTF}\_{\text{L,R}} \left( \theta, \phi, f \right) \right| = \left| \text{HRTF}\_{\text{L,R}} \left( \theta, \phi, f \right) \right| \exp\left[ j \arg \text{HRTF}\_{\text{L,R}} \left( \theta, \phi, f \right) \right], \tag{5}$$

and the HRIR value:

2 Advanced Topics in Measurements

reproduced (Hartmann & Wittenberg, 1996; Horbach et al., 1999; Hen et al., 2008, Plaskota & Kin, 2002; Plaskota et al. 2003). Since there are many sound source locations in the space surrounding the listener many HRTFs are needed to accurately reproduce the location of the

The function describing the direction-dependent acoustic filtering of sounds in a free field by the head, torso and pinna is called HRTF. Although it is obvious that the linear dependence between Interaural Time Difference (ITD), Interaural Level Difference (ILD) and the perceived location in space needs to be predicted, it is less obvious how the spectral structure and the location in space can be mathematically interrelated (Cheng & Wakefield, 2001). The first step towards understanding the significance of the signal spectrum in directional hearing was an attempt at physical modeling and empirical measurement followed by computer simulations of the ear's frequency response depending on the

Formally a single HRTF function is defined as an individual right and left ear frequency response measured in a given point of the middle ear canal. The measurement is conducted in a far-field of the source placed in a free-field. Typical HRTFs are measured for both ears in a particular distance from the head of the listener for several different points in space. Thus the transmittance function related to the head depends on the azimuth angle, elevation angle and the frequency, and apart from that it has a different value for the left ear (L) and

In fact a measured transmittance function includes also a certain constant factor. This factor characterizes the measurement conditions – the measurement chamber characteristic and the measurement path. This is a reference characteristic, and the value of this parameter is determined by measuring the impulse response without the presence of the measured subject. Therefore by additionally taking into consideration the reference characteristic the

*h t s t c t HRIR t L R*, ,

– impulse response related to the head.

surrounding the listener, and it differs for the left and right ear: *c t L R*,

*L R*

– impulse response by the entrance to the ear canal,

In some conditions it can be assumed that *c t* is constant and not influenced by the measurement point's position in space. Then the *c t* value is a mean measurement result for several different azimuth angles and elevation angles. But if the measurement chamber does not fulfill the conditions of the anechoic chamber or in the room are present some elements which cause generating undesirable reflections, the *c t* factor is influenced not only by the time, but also by the position of the measurement point in the space

> , ,

, , *f* . The HRTF's time-domain equivalent is the Head-

 

, , , (1)

 , , 

value can be measured for every

. In order to

direction. The measured frequency response of the ear is subject to further analysis.

 

result of the transmittance function can be presented as

increase the accuracy of the measurement the *c t L R*,

*s t* – measurement signal,

 , , 

*c t* – impulse response of the measurement system,

sound source in this space.

for the right one (R): *HRTFL R*,

where: , , , *L R h t*

 

*HRIR t L R*, , , 

Related Impulse Response (HRIR).

$$HRIR\_{L,R}\left(\theta,\phi,t\right) = \mathcal{F}^{-1}\left[HRTF\_{L,R}\left(\theta,\phi,t\right)\right],\tag{6}$$

where: <sup>1</sup> *F* – inverse Fourier transform.

It has been empirically proven that HRTFs are minimum-phase, therefore minimum-phase FIR filters are used to simplify the HRTF description interrelated (Cheng & Wakefield, 2001). Firstly, minimum-phase requirement allows to explicitly define the phase on the basis of the amplitude response. This is a consequence of the fact that the logarithm of the amplitude response and phase response in a casual system are related by the Hilbert transform. Secondly, the minimum-phase requirement allows to isolate the information about the ITD from the FIR characteristic describing the HRTF. When the minimum-phase filter has the minimum group-delay property and the minimum energy delay, most of the energy is accumulated at the beginning of the impulse response and the appropriate for the left and right ears minimum-phase HRTFs have zero delay.

In order to achieve the characteristic of the hearing impression related to a particular point in space there are three values to be measured: the left ear amplitude response, right ear amplitude response, and ITD. The characteristics of the filter include both the ITD and ILD information: time differences are included in the phase characteristic of the filter, whereas the level differences correspond with the total power of the signal transmitted through the filter interrelated (Cheng & Wakefield, 2001). The interaural time difference can be calculated by many various measurement methods: as a result of measurement with the participation of people, a result of the dummy-head measurement, simulations performed on the spherical and elliptical models, calculation based on Woodsworth-Slosberg formula (Minnaar et al., 2000; Weinrich, 1992).

Conducting the measurements for a big number of people is a complicated issue (Møller et al., 1995; Møller et al., 1992). The head-related transmittance functions show a great individual variability: the discrepancy between the measurement results reaches about 3 dB

System for High Speed Measurement of Head-Related Transfer Function 5

millimeters over an ear entrance, an ear entrance, a few millimeters under an ear entrance, directly over the tympanic membrane (Pralong & Carlile, 1994). Additionally, the ear entrance closing influence on the measurement result is considered. It was found out that a smaller individual variation is obtained in measurements with closed ear entrance (Møller et al., 1995). It was also determined that the ear canal transfer function is independent of sound

The parameters of electroacoustic transducers have a great influence on the measurement result, especially a frequency response. The frequency responses of microphones are more important than the frequency responses of loudspeakers (Plaskota, 2003). It is suggested to use loudspeakers with a frequency response without large deeps (Møller et al., 1995).

In the studies there are informations available about used signals during the HRTF measurements. One of the applied signals is the Maximum Length Sequence (MLS) (Møller et al., 1995). It is possible to use Golay codes (Algazi et al., 2001), but difficulties in results interpretation are known (Zahorik, 2000). In anechoic chamber, the use of chirp signal is adequate to measurement conditions. It can be supposed that in a non-anechoic chamber the impulse signal is applied. It comes from a necessity of providing good measurement

The HRTF measuring device is built for a special group of test participants. It is assumed that the measurement will be made for people with severe vision problems (Bujacz & Strumiłło, 2006; Dobrucki et al. 2010). Therefore, the device is designed to reach many demands such as the highest automation of measurements which assures a short measurement time (ca 10 minutes) and offers great ease of manipulation. The participant of the test should feel comfortable during the measurement process and should be given sufficient information on each part of the measurement. To reach these demands, the device is equipped with a bidirectional communication system allowing the participant to report the problem at any time. In addition to voice communication, a visual control of the room is provided. It is possible to monitor the test room using a camera mounted on an arc with

To provide a short measurement time the HRTFs are measured for both ears simultaneously. The way sound sources are configured significantly shortens this time too. The loudspeakers are mounted on vertically positioned arc (see Fig. 1). It allows to measure the range of vertical angles from -45° to +90° in one chair position. In certain points in the space of the room the measurement is made by switching the measurement signals to

The number of measurement points for elevation angles is adjusted by changing the number and position of the loudspeakers. On the other hand, the number of measurement points for horizontal angles depends on the size of the rotation step of the chair. The rotation of the chair is controlled by a stepper motor which assures high horizontal resolution. Default vertical resolution is 9° in regular sound source positions. Assuming the same horizontal resolution the number of measurement points is 640. The measurement in 16 points for one horizontal angle and simultaneous measurements for both ears allows to conduct the whole

source position in the space around the listener (Bovbjerg et al., 2000).

conditions.

loudspeakers.

**4. Measuring system** 

**4.1 Conception of measuring system** 

subsequent loudspeakers by an electronic switch.

for the frequency to 1 kHz, 5 dB for the frequency to 8 kHz and about 10 dB for the higher frequencies. The first reason is an obvious dependence on individual physical body differences. Other reason are the measurement errors which are hard to be calculated in the final results – e.g. the error resulting from the differences in positioning the head in relation to the sound source or the differences in placing the measurement microphone in the ear canal. The individual HRTF variable is lower for the measurements conducted with a closed ear canal than for the measurements with an open ear canal.
