Time Efficient Measurement Method for Individual HRTFs

Pascal Dietrich, Bruno Masiero, Martin Pollow, Benedikt Krechel and Michael VorlanderInstitute of Technical Acoustics, RWTH Aachen University, Neustraße 50, 52056 Aachen, Email: pdi@akustik.rwth-aachen.de

Introduction

An optimized multi-channel measurement setup for theacquisition of individual HRTFs in anechoic environ-ments has been developed as shown in Figure 1. Thiskind of measurement is usually time-consuming, if highspatial resolution is required. A recently introduced tech-nique allows simultaneous playback of multiple exponen-tial sweeps through several sound sources by even con-sidering slightly non-linear behavior [1]. This approachdirectly leads to a significant reduction of the requiredmeasurement duration. A different approach uses a con-tinuous measurement method of a rotating person witha single or several loudspeakers to speed up the HRTFmeasurement on horizontal rings [2]. This contributionintroduces a new optimization strategy for the excitationsignals, regarding measurement duration and achievedaccuracy of the measurement.

Figure 1: HRTF arc in the anechoic chamber at ITA.

Multiple-exponential sweep method

Acoustic systems are usually assumed to be linear timeinvariant (LTI). Hence, linear system theory is applicablealong with various excitation signals for correlation mea-surement techniques. Exponential sweeps are known tohave advantages when it comes to non-linear systems [3].Non-linear behavior of the system is observed as anti-causal impulse responses hharm,i for different harmonicorders i separately. The multiple-exponential sweepmethod (MESM) proposed by Majdak is applicable forweakly non-linear systems [1]. By this method the mea-surement duration can be significantly reduced when thenumber of sound sources L is high. Majdak introducedtwo different strategies. One called overlapping, where

the harmonic impulse responses appear between the im-pulse responses of interest; and another strategy calledinterleaving, where the impulse responses of interest aregrouped together and then a group of all non-linear im-pulse responses follows. A combination of both strate-gies is given with an optimization algorithm by Majdakas well. The measurement duration of N multiple sweepmeasurements with a sweep of length τsweep and a silencein the end of length τstopMargin is given by

τMESM(L) = (L− 1)τwait + τsweep + τstopMargin, (1)

compared to the duration of a conservative, discrete mea-surement

τseparate(L) = L(τsweep + τstopMargin). (2)

The theoretically achievable reduction of measurementtime for a large number of loudspeakers can be expressedas

limL→∞

τMESM(L)

τseparate(L)=

τwait

τsweep + τstopMargin. (3)

Usually the length of sweeps lies in the length of 0.2 sfor very short and 2 s for moderately long sweeps. Theconstant τwait depends on the sweep rate, the maximumorder of non-linearities and the length of the measuredimpulse response. For HRTF measurements in suitableanechoic environments the range of the impulse responsehRIR is estimated as 20 ms to 100 ms.

The MESM method can yield impulse responses thathave the same quality as separately and consecutivelymeasured impulse responses. The signal to noise ratioand the temporal and spectral structure of both resultsremain the same if the following requirements are ful-filled: The system has to be at most weakly nonlinear,i.e. the number of harmonic impulse responses has to besmall. In case non-linearities are observed, the level hasto be kept constant during both measurement and cali-bration – note that this constrained has not been statedin the original paper. The length of the impulse re-sponse should be much smaller than the smallest timeτwait between two subsequent sweeps. Once the weaklynon-linear loudspeakers playback the MESM signal nofurther weak non-linearities are allowed, i.e., the micro-phones and preamplifiers have to be driven in a straightlinear range only.

Optimization Strategy

A new optimization strategy is used taking into accountthe expected structure of the theoretical impulse responseof the system measured with an exponential sweep asshown in Figure 2. The impulse response of the loud-speaker and the HRTF is very short with an approxi-mate duration of 4 ms. This part of the impulse response

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carries the important information and shall never be su-perposed by harmonic impulse responses. It is there-fore called avoid zone. On the other hand, the impulseresponse of the hemi-anechoic chamber of the instituteshows reflections from the floor, supports, mounts anddoors in the order of 40 ms. The remaining impulse re-sponse of the room does not carry any useful informationand can therefore be used as a place holder for the har-monic impulse response. This observation enables us tofind optimized sweep parameters to fulfill the require-ment by using twait very close to 40 ms. As this timeis usually much smaller than the measurement signalthe MESM reduces the measurement time dramatically.Since the subject has to be measured under N differentorientation angles the measurement time of the optimizedMESM method reads as N · τMESM(L).

time

avoid zone

noise floor

tIR

tRIR

Figure 2: Temporal structure of an impulse response mea-sured with an exponential sweep.

Results

The frequency response of the transfer function from oneloudspeaker to one ear of the artificial head is depictedin Figure 3. The results show no noticeable deviationsand therefore the optimized MESM is considered valid.The measured HRTF using a continuous rotation of thesubject is compared with the discrete rotation in Fig-ure 4. The excitation signal remains the same but it isdirectly concatenated for the continuous rotation. TheHRTF shows only slight deviations and a small rotation.

-50

-40

-30

-20

-10

0

10

20

Modulusin

dB

60 100 200 400 1k 2k 4k 6k 10k 20k

Frequency in Hz

MESM [dB re 1]sweep [dB re 1]

Figure 3: Comparison of sequential sweep measurementswith MESM measurements (only one direction is plotted,MESM shifted by +10 dB).

Figure 4: Comparison of HRTF with optimized MESM andcontinuous rotation (top: sequential, bottom: continuous,left: 1 kHz, right: 4 kHz).

Conclusion

The adaptation of the MESM by using a detailed modelof the impulse response and a new optimization strategyshows great potential for realistic anechoic environments.The non-linearities caused by the loudspeaker are consid-ered. The signal to noise ratio remains the same. Therequired measurement duration has been reduced from80 minutes for the conservative method to 4 minutes forthe optimized MESM and sequential rotation of the sub-ject. The spatial resolution is 7.5◦ in elevation and 3.75◦

in azimuth. No loudspeakers are available at elevationangles 150◦ to 180◦. The combination with the contin-uous measurement by continuously rotating the subjectyields a reduced measurement time of only 2 min withthe same resolution.

Acknowledgments

The authors would like to thank Piotr Majdak for valuablediscussions and Johannes Klein for first testing of the routinesand photography. The routines have been implemented inMATLAB using the ITA-Toolbox [4].

References

[1] P. Majdak, P. Balazs, and B. Laback, “Multiple exponen-tial sweep method for fast measurement of head-relatedtransfer functions,” J. Audio Eng. Soc., vol. 55, no. 7-8,pp. 623–637, July-August 2007.

[2] G. Enzner, “3d-continuous-azimuth acquisition of head-related impulse responses using multi-channel adaptivefiltering,” in IEEE Workshop on Applications of SignalProcessing to Audio and Acoustics, 2009.

[3] S. Muller and P. Massarani, “Transfer-function measure-ment with sweeps,” Journal of the Audio Engineering So-ciety, vol. 49, pp. 443–471, 2001, printed.

[4] P. Dietrich, M. Guski, M. Pollow, M. Muller-Trapet,B. Masiero, R. Scharrer, and M. Vorlander, “ITA-Toolbox– An Open Source MATLAB Toolbox for Acousticians,”in Fortschritte der Akustik – DAGA, 2012.

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