Spectrum Analysis

No HRTF of the B&K Dummy head used in the measurements was available for the BRIR calculations in ODEON. ODEON recommends to use the HRTF Subject 021

0 10 20 30 40 50 60

Figure 5.3: Early part of BRIR Left channel, L2S1, measured and simulated, without reection

Figure 5.4: Frequency response of L2S1, before and after the adjustment for the simulation, which is based on the standard Kemar head. However, ODEON did provide a set of 46 other dierent HRTFs from human subjects of the Cipic HRTF database. To get the HRTF that most closely resembles the dummy head used for the measurements, all HRTFs of the database were compared to the measured HRTF.

The measured HRTF was obtained by truncating the BRIRs to the direct sound (samples 200 to 450), cutting o all reection. The HRTF with the lowest mean deviation from the measurement (Subject 012) was used for the simulations. The

frequency response for the direct sound of the measurement and the simulations for L2S1 done with HRTFs of subject 012 and the recommended 021 can be seen in Fig.

5.5. Both the measurement and the simulations used the Echo source.

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Figure 5.5: Frequency Response of the direct sound of the simulated and measured BRIR for L2S1, Subject 012 and 021

The modelled source used for the ODEON simulations was based on an available rotation measurement of the Echo source performed by Constant Hak. This simulated source was compared to this measurement. Information on the microphone used to record the rotation measurement was not available. The simulations are performed in a modelled anechoic room using the so-called unity-HRTF. The results can be seen in Fig. 5.6. Using this lter, the receiver in ODEON is modelled as a omnidirectional microphone instead of a dummy head. Since no rotation measurement could easily be simulated in ODEON, the rotation measurement audio had to be adjusted to be compared to the simulation. The rotation measurement clearly showed one peak in power, indicating that the source was pointing directly at the microphone. This part of the measurement was cut out and used for the comparison with the simulation.

The BRIR for the anechoic room is recorded at the (relative) position L2S1. Both the simulation and measurement show a similar trend with less power for the lower frequencies and an increasing power for the higher frequencies. However, the power for the middle frequencies from the 250 to the 1000 Hz octave bands is higher for the rotation measurements compared to simulations.

This dierence for the lower frequencies is not shown when comparing the measured and simulated BRIRs in Fig. 5.7.a. Here, the measured BRIR has more power in the lower frequencies than the simulations. Some errors could be caused by the ODEON Software. Generally, geometrical acoustics can be applied for frequencies above the so-called Schroeder Frequency [63]. The Schroeder frequency fsis calculated by the following equation [6]:

f > fs= 2000 · rT

V

63Hz 125Hz 250Hz 500Hz 1000Hz 2000Hz ,4000Hz

Figure 5.6: Frequency response of the Echo source, omnidirectional microphone

. In the case of this sports hall, this leads to an approximate

fs= 2000 ·

r 3.55

42.16 · 24.64 · 6.94≈ 44Hz .

This value is below the frequency range that is investigated with this study. It is remarkable though, that the simulated BRIR has more power in the lower frequencies than the measured. Simulated and measured BRIRs were also compared in the study of Zhu et al. [74]. Here, the simulations have considerably less power in the lower frequencies than the measurements. In this study, the speech, trumpet and drums samples were used. Frequency responses of the BRIR of L2S1 convolved with the speech, trumpet and drum samples can be seen in Fig. 5.7 b, c and d. The dierences between the simulation and measurement may be increased due to the spectrum of the sample used for convolution. Still all three samples show the largest deviations for the lower frequencies.

5.4 Results

As can be seen in Fig. 5.8, the simulated values for T30 deviate a lot from the measured values. It seemed interesting to compare the listening test results of aural-isations with these 'incorrect' T30 values with auralaural-isations of which the T30 values matched those of the measurements. A way to correct this dierence in T30 is to adjust the absorption coecients. This method is referred to as calibration [75]. The absorption coecient of the largest surface is being adjusted until similar T30-values are found [75], which in the case of this sports hall is the ceiling or oor. Since the

oor is made only of concrete and has low absorption coecient values, it would seem illogical to ajdust and increase the absorption coecients of this material.

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Figure 5.7: Comparison of spectra, measured vs simulated: a. BRIR L2S1 b. Human speech L2S1 c. Trumpet L2S1 d. Drums L2S1

The average T30-values of six positions (L1S1, L1S8, L1S14, L2S1, L2S10, L2S16) were used. The original and adjusted absorption coecients for the ceiling can be found in Table 5.3. It is clear that the α-values have been changed drastically and might not be realistic anymore for this surface material. However, it leads to almost identical T30-values, as can also be seen in Fig. 5.8. The spectra of the calibrated and non-calibrated models are compared in Fig. 5.9. Here, the eect on the spectrum of this BRIR before and after calibration appears to be minimal.

Table 5.3: Absorption coecients of the ceiling - Paper settings and calibrated

Surface 125Hz 250Hz 500Hz 1K Hz 2K Hz 4K Hz

Ceiling - base value [19] 0.29 0.68 0.57 0.40 0.18 0.05

Ceiling - calibrated 0.52 0.09 0.09 0.12 0.53 0.40

125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz Frequency (Hz)

1 1.5 2 2.5 3 3.5 4

T30 (s)

Measurement ODEON - Paper Settings ODEON - calibrated

Figure 5.8: T30, Measured, simulated and calibrated

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Frequency (Hz) -60

-50 -40 -30 -20 -10 0

dB

Before calibration After calibration

Figure 5.9: Spectra of the simulated BRIR of L2S1, before and after calibration