Computational Systems for Sound Fields, as Tools in Design and Diagnosis

Chapter 3 Diagnostic System for sound fields in a Room
3.1. Introduction
In order to measure orthogonal factors, SPL, DT₁, T_sub, IACC, t_IACC, and W_IACC [37-42], and also the running ACF of sound field at each seat in a scale model as well as in a real auditorium, a diagnostic system is developed. Based on the model of auditory-brain system which consists of the autocorrelation mechanism, the interaural crosscorrelation mechanism between the both auditory pathways, and the specialization of human cerebral hemispheres as shown in Figure 3.1 [37], a diagnostic system was designed.

Figure 3.1. A model of auditory-brain system.

The system works on PC for Windows with an AD & DA converters, there is non need for special additional devices. After obtaining the binaural impulse responses, four orthogonal factors including the SPL, the initial time delay gap between the direct sound and the first reflection, the subsequent reverberation time and the IACC are analyzed. These factors are used for the calculation of both the scale values of global and individual subjective preferences. In addition to the four factors, two more factors, t_IACC and W_IACC as defined in Figure 3.2, extracted from the interaural crosscorrelation function can be figured out for evaluating the image shift of sound source and the apparent source width [42], respectively.

Figure 3.2. Definitions of the IACC, t_IACC and W_IACC in the interaural crosscorrelation function.

Also, the averaged sound energy, F(0), the effective duration, t_e, defined by the delay at which the envelope of normalized ACF becomes 0.1 (Figure 3.3), and fine structures of autocorrelation function of sound signals including the magnitude of first maximum, f₁, and its delay time, t₁, of source signals are analyzed. In order to examine effects of reflectors' array above the stage in a 1/10 scale model of auditorium, the IACC measurements are demonstrated here.

Figure 3.3. A practical example of determining effective duration of ACF defined by the ten-percentile delay, with the straight line-fitting envelope of ACF from 0 to -5 dB.

3.2. Outline of a Diagnostic system
Because the complex requirements made the system difficult to evaluate, an advanced diagnostic system and a high-power computer was used. The measuring system was utilized to obtain the binaural impulse response at each listening position. The sound was created using an omni-directional loudspeaker fed with a maximum-length signal produced by a diagnostic system in a notebook PC. The period of maximum-length signal (MLS) was between 1024 and 524288 samples, and the sampling rate can be changed between 8 kHz and 48 kHz. The acoustic signal amplified from the two microphones placed at the entrances of ears of a 1/10 scale model of dummy head (a sphere with the diameter of 25 mm) was sampled after passing through a low pass filter (Figure 3.4).

Figure 3.4. A block diagram of the measurement system.

The binaural-impulse-response measurement may be performed by a summation of the output data from the linea system, without any multiplication operation [43, 44]. The measurement was done automatically within only a few seconds by pushing a single button. This is realized by the logic that the Dt₁ is obtained automatically (Appendix B). It took another few seconds for the analysis of the orthogonal acoustic factors and the scale value of the subjective preference. And at the same time this program can took the result to compute the acoustic parameters and prepare the reports.

3.3. Application of the Diagnostic system (I) for the Kirishima International Concert Hall after Construction

A. Comparison between Simulated and Measured Values of Orthogonal Factors
    The Kirishima International Concert Hall contains 770 seats and has a volume of 8,475 m3. In order to increase the number of seats close to the stage, the width of the hall was increased from 17.9 m to 19.7 m (1.8 m) just before construction.
    The physical factors at each seat were measured using a maximum length sequence sound signal [33]. The signal was reproduced by an omnidirectional dodecahedron loudspeaker placed 1.5m above the stage floor. The sound source was located either at the center of the stage (S1) or 2 m to the side of the center (S2). Sixty-four seats were selected to test the source location S 1 and 6fty-Gve seats for the source location S2. At each seat, the acoustic signals were recorded by two small microphones at the entrances of the ear canals of a real person. In order to obtain the impulse responses, the signals were analyzed using the Hadamard Transformation. Using the impulse responses at both ears, the physical factors LL, Dt₁ , T_sub , IACC, and A-Value were calculated for all octave bands with center frequencies between 125 Hz and 4 kHz.
    The measurements of the physical factors (LL and T_sub at frequencies of 500Hz, IACC for white noise, Dt₁, and A-Value) for S2 are shown in Figure 3.5.

Figure 3.5. Results of measured values of physical factors for source position S2: (a) Contour lines of equal relative-listening level (500Hz) [dB]; (b) Contour lines of initial time delay gap between the direct sound and first reflection excluding the floor reflection [ms]; (c) Values of reverberation time (500Hz); (d) Contour lines of equal IACC (for white noise) (e) Contour lines of equal A-value.

The listening levels indicated are relative to those at the front seat near the centre line. The range of the values is similar to that of the calculated results, that is, 8.5dB for Sl and 6.5 dB for S2. The largest initial time delay is 29ms and is not much different from the calculated value (27ms), in spite of the change in hall width. The reverberation time T_sub Obtained by the decay rate between -5 dB and -20 dB is almost constant throughout the hall, and has a range of j=0.05 s (unoccupied). It is estimated to be about 1.75 s when the hall is occupied, which is close to the design goal (1.8 s). The IACC values for frequencies above 500 Hz are less than 0.5 throughout the hall, and the interaural time delay t_IACC for S1 is constant at zero for almost all seats. Generally, the IACC at each seat is smaller for source position S2 than for S 1. With regard to the physical factors of upper level seating, the contour lines between calculated and measured values cannot be compared because there were few measuring points. The differences between calculated values and measured values throughout the seats measured (23 points) are as follows; LL: ±1.0 dB, Dt₁: ±3.0ms and IACC: ±0.05.
    In spite of the change (about 10 percent) in the width of the hall, reasonable agreement between calculated and measured values of the four physical factors was obtained in the design Process.

B. Remarks
    In this study, the system had been developed, which can measure four orthogonal factors including the SPL, the initial time delay gap between the direct sound and the first reflection, the subsequent reverberation time and the IACC, in order to diagnose sound fields of each seat in the concert hall at its completion based on the model of auditory-brain system.
    The usefulness has been revealed by comparison between the orthogonal factors obtained by actual measurement at Kirishima concert hall's completion and the orthogonal factors obtained by simulation at the planning stage.

3.4.

Application of the Diagnostic System (II) for the 1/10-Scale Model of the Tsuyama Music Cultural Hall

A. Effects of Reflectors Above the Stage
(1) Procedure
The diagnostic system developed may examine effects of scattered reflections of complex boundary conditions of the room. The reflectors above the stage are designed mainly for the performer obtaining the preferred reflections according to the program sources. We measured the IACC of sound field at each seat to find effects of reflectors' array above the stage [46]. The effective direction of reflections to listeners for the 2000 Hz range is centered on +- 18 degrees from the median plane, which might be realized by the reflectors above the stage [37]. Therefore, the IACC of the 2000 Hz-frequency band is selected here to be examined.
In order to obtain reliable results, measurements were repeated several times until obtaining the same results of the binaural impulse responses. The sound is produced using an omni-directional loudspeaker fed with the MLS produced by the diagnostic system in a notebook PC. Figure 3.6 shows the window on PC of actual diagnostic system with the data obtained from the impulse responses. In the measurement, a special attention should be made to maintain a suitable value of the signal to noise ratio adjusting the power level of the loudspeaker.

Figure 3.6. An example of display window of the diagnostic system, with binaural impulse responses.

(2) Results
As mentioned above, in order to examine effects of reflectors' array on the IACC for the 2000 Hz range at 15 seating positions shown in Figure 3.7, measurements were performed with and without reflectors above the stage.

Figure 3.7. Measured IACC for the 2000 Hz-frequency band with reflectors above the stage.

As indicated in this figure, the location of the sound source is marked by a star, and triangular reflectors` arrays [46] are installed above the stage. Figure 3.8 shows the measured results of the IACC without reflectors, and Figure 3.7 shows those with reflectors` array. The IACC values of the 2 kHz-frequency band for a real room were measured at the 20 kHz frequency band in the 1/10 scale model.

Figure 3.8. Measured IACC for the 2000 Hz-frequency band without reflectors above the stage.

As shown in these figures, the reflectors decrease results of the IACC at the 9 measuring points, so that acoustic quality is much improved. Especially, the decrement of IACC values was remarkable in the frontal area close to the stage in audience floor except for the center, due to the reflections from above the stage to the listeners.

B. Remarks
It is shown that measurements in the 1/10 scale model for acoustic parameters by the diagnostic system may prove effects of reflectors' array and other scattering elements which may not available by calculation at the design stage. In order to examine the sound fields after the construction of the auditorium, the diagnostic system measuring orthogonal factors may be applied. Also, keeping the subjectively optimal conditions, this system may be applied for the automatic control of sound fields by the use of electro-acoustic systems.

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