A system for measuring the directional room acoustical parameters

Applied Acoustics 62 (2001) 203±215 www.elsevier.com/locate/apacoust

A system for measuring the directional room acoustical parameters Hiroyuki Okubo *, Masamichi Otani 1, Ryo Ikezawa 1, Setsu Komiyama, Katsumi Nakabayashi NHK Science and Technical Research Laboratories, 1-10-11 Kinuta Setagaya, Tokyo 157-8510, Japan Received 4 August 1999; received in revised form 12 April 2000; accepted 27 June 2000

Abstract A new system has been developed for measuring the directional parameters of room acoustics. The lateral component (LC), front to back ratio (FBR) and left to right ratio (LRR) of directional room impulse responses are easy to measure with this system. The system was used to take measurements in a multi-purpose hall (for concerts, conventions and exhibitions). The directional parameters of early re¯ection were sensitive to room shape, wall materials and the positions of seats. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Room acoustics; Sound ®eld measurement; Directional parameters

1. Introduction It is well known that spatial impressions di€er depending on where one sits in an auditorium, because the distribution of the early re¯ection depends on the position of the seat. In recent decades, various directional parameters based on early re¯ection have been considered. Marshall proposed the importance of early lateral re¯ections in 1967 [1]. Barron and Marshall proposed the ``lateral energy fraction (Lf),'' corresponding to ``spatial impression'' [2]. Morimoto and Iida proposed that the front/back ratio (FBR) of early re¯ection is needed because this value a€ects the psychological evaluation of the sound ®eld [3]. In addition, the left/right ratio (LRR) of early re¯ections may also be useful for estimating di€erences between seats. The * Corresponding author. Tel.: +81-3-5494-2346; fax: +81-3-5494-2238. E-mail address: [email protected] (H. Okubo). 1 Present address: NHK Broadcasting Center, 2-2-1 Jin-nan Shibuya, Tokyo 150-8001, Japan. 0003-682X/01/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(00)00056-6

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directional parameters re¯ect the geometrical distribution of sound re¯ection passage, so these are useful for the design of room shapes, re¯ectors and the arrangements of seats. Some techniques for measuring directional response have been considered for use in evaluating directional sound re¯ections. First, Thiele [4] and Meyer [5] investigated di€usitivity, using the parabolic microphone. Flanagan [6] and Nishi [7] developed array-microphones to capture directional impulse responses. These systems, however, must be large to achieve an ideal directional pattern over a wide frequency range. Yamasaki et al. investigated the distributions of virtual image sources and directivity patterns of some concert halls by utilizing a correlation technique from waveform information obtained from the four point microphones [8,9]. With this method, the details of the individual structure of the early re¯ections are analyzed, but quantitative discussion based on the directional parameters is not mentioned. Jordan proposed a simpli®ed method to measure lateral eciency (LE) by utilizing a ®gure-of-eight microphone [10]. In this method, however, the accurate calibration of the ®gure-of-eight microphone and omni-directional microphone is indispensable, and FBR and LRR cannot be estimated. We have developed a new measuring system by which the individual directional energy (front, back, left and right) of early re¯ections can be measured. The lateral component (LC), the front/back ratio (FBR) and left/right ratio (LRR) of early re¯ections are easy to measure using this system. The system has also been used to make measurements in a multi-purpose hall. The directional parameters measured there were sensitive to room shape, wall materials and the positions of seats. This paper is set out in six sections. The next section describes the de®nition of the directional parameters we handle. In the third section, the synthesis of the directional pattern for measuring directional impulse responses is explained. In the fourth section, the outline of the measuring system is described. And in the ®fth section, we show example of directional parameters as measured in an auditorium. The ®nal section is the conclusion. 2. The directional room acoustical parameters The directional room acoustical parameters are de®ned as follows. The LC value is the ratio of the lateral component of early re¯ection energy: „ Tÿ LC ˆ 10  log10

0


p2L …t† ‡ p2R …t† dt „T 2 0 pO …t†dt

…dB†

…1†

The FBR value is the ratio of front/back early re¯ection energy: „T

FBR ˆ 10  log10 „ 0T

p2F …t†dt

2 0 pB …t†dt

…dB†

…2†

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The LRR value is the ratio of left/right early re¯ection energy: „T

LRR ˆ 10  log10 „ T0

p2L …t†dt

2 0 pR …t†dt

…dB†

…3†

where p2O …t†, p2L …t†, p2R …t†, p2F …t† and p2B …t† are the omni, left, right, front and back directional components of power, respectively. The relation between the incident angle of re¯ection sound and these directional components is shown in Fig. 1. T is 80 ms. These directional components are calculated over the octave bands from 63 Hz to 8 kHz by convolving with an octave band ®lter when frequency characteristics are needed. 3. Synthesis of the directional pattern 3.1. Synthesis of the directional pattern The directional energy components (front, back, left and right) of early re¯ections should be measured individually to calculate the directional parameters de®ned in Section 2. The ideal microphone directivity for the measurement is one side of the ®gure-of-eight, but this is dicult to realize. The cardioid pattern is easy to realize with a microphone, but this directional pattern has insucient decrease at 90 (only ÿ6 dB). As the direct sound intermixes when its main lobe is aimed in lateral directions, the LC value is overestimated. The new method of multiplying cardioid and ®gure-of-eight responses is proposed to solve this problem. The directional pattern

Fig. 1. Relation between incident angle of re¯ection sound and directional parameters.

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synthesized by this new process is shown by the thick line in Fig. 2. It should be noted that the radius in Fig. 2 shows the dimension of power. The polar pattern becomes narrow compared with the cardioid-pattern, and is close to one side of the ®gure-of-eight pattern. The signals synthesized by this multiplying process have an order of power, good for obtaining energy values such as LC, FBR and LRR. 3.2. Error estimation by simulation In this section, the error of the new method is estimated using the Ray±Tracing simulation. Fig. 3 shows the estimation of LC values using the new method. Seven simple room shapes (rectangular, cubic, longitudinal tunnel, transverse tunnel, fan shaped, reverse fan shaped and rectangular with re¯ectors) which have the same volume (9000 m3) and the same reverberation time (1.5 s) were supposed and, using the Ray±Tracing method, the simulation of LC values was carried out. The theoretical LC value and the LC values of estimated directional patterns (the cardioid pattern and the new directional pattern) were calculated for each room shape. The theoretical value of the LC is calculated by the following method. It is assumed that the early re¯ection energy in the left and right direction is measured separately with a microphone which has a directional pattern of one side of the ®gure-of-eight pattern.
2 „ Tÿ dt 0 p…t†
cosp…t† LC…theoretical† ˆ 10  log10 „T 2 0 p …t†dt

…dB†

…4†

where p…t† is the individual re¯ection which comes from p…t† degrees (0 lies in the lateral direction) (see Fig. 1), at t. T is 80 ms. The LC values with this new method and by the cardioid method are estimated by the following:

Fig. 2. Directional patterns of microphone probe.

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„T 2 p …t†dt LC ˆ 10  log10 0„ Tlateral 2 0 p …t†dt p2lateral …t†

…dB†

207

…5†

   1 ‡ cosp…t† 2 1 ÿ cosp…t† 2 for the cardioid pattern ˆ p…t† ‡ p…t† 2 2 

    1 ‡ cosp…t† 1 ÿ cosp…t† p2lateral …t† ˆ p2 …t† cosp…t†  ‡ cosp…t†  for the new method: 2 2

Each LC value in Fig. 3 is averaged over the octave bands from 250 Hz to 2 kHz. For all seven room shapes, the errors using the new pattern are very small (under +/ÿ1dB) compared with those with the cardioid pattern. The di€erence limen of the lateral energy component is estimated to be about 3dB [11], so the directional energy components can be measured with sucient accuracy by new method.

Fig. 3. Estimation of LC values.

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4. Measuring system 4.1. The system's outline This section describes the outline of the measuring system and the arrangement of the microphone probe. The layout of this system is shown in Fig. 4. The system consists of the microphone probe, the capturing part (consisting of the pre-amp, electrical directional pattern synthesis unit and optical transmitter) and the processing part (consisting of the optical receiver, audio interfaces, DSPs (digital signal processors) and control software). Five omni-directional pin-microphones for picking up sound signals in an auditorium are put together as a microphone probe. The diameter of this probe is 10 cm, which makes it easy to carry in one hand. The arrangement of the microphones is shown in Fig. 5. The microphone situated in the center picks up omni-directional signals. The di€erence between the two microphones arranged on opposite sides (front and back) forms a ®gure-of-eight response which corresponds to the forward and backward directions. The di€erence between left and right microphones is also a

Fig. 4. The layout of the measuring system.

Fig. 5. The arrangement of the microphones.

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®gure-of-eight response which corresponds to the left and right directions. These ®gure-of-eight responses are synthesized suciently in the frequency range which satis®es l  d, where ``l'' is the wave length of an observed signal and ``d'' is the distance between two microphones. The upper frequency limit is given by this condition. For example, the upper frequency limit is about 8.5 kHz (l ˆ 4:0 cm) when the distance between the microphones is 2 cm. The frequency response decreases as the frequency becomes lower [Fig. 6(a)]. Even if this characteristic is equalized, the signal to noise ratio decreases at lower frequencies. The lower frequency limit is given by this condition. The lower frequency limit is about 200 Hz (the signal to noise ratio is under 40 dB below this frequency ) when the distance between the microphones is 2 cm. The frequency responses of omni-directional signals, the ®gure-of-eight signal after equalization, and the noise level of a ®gure-of-eight signal after equalization are shown in Fig. 6(b). The di€erences between omni-directional response and ®gure-of-eight responses after equalization are small, because the ®ve omni-directional microphones are selected carefully and their characteristics are almost the same. A sucient signal-to-noise ratio (over 40 dB) is achieved between 200 Hz and 6 kHz, when the distance between the microphones is set at 2 cm. If a

Fig. 6. Frequency responses of the microphone probe.

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sucient signal-to-noise ratio is needed at lower frequencies, the distance of microphones ``d'' can be adjusted by up to 10 cm on the probe. 4.2. The measuring sequence Measurements are made in a sequence, with each part of the system working as described below. (a) The TSP (Time stretched pulse) signal [12] synthesized in the processing part is the output. The TSP signal is the most appropriate signal, consisting of all frequency signals, and improves the signal-to-noise ratio. Less time is, therefore, required than when using white noise signal (such as the cross-spectral method) which needs a long averaging time to improve the signal to noise ratio. (b) The TSP signal is ampli®ed and radiated from an omni-directional loudspeaker system, such as a dodecahedron loudspeaker [13], into the auditorium. (c) Electrical combinations of the ®ve microphones produce an omnidirectional (O) and two ®gure-of-eight (X : back and forth, Y: left and right) patterns in the capturing part. These signals are transmitted to the processing part through an optical cable. (d) The software for signal processing calculates omni-directional and ®gure-ofeight impulse responses for the auditorium by convolving O, X and Y signals with the ITSP (Inverse TSP) signal. They are divided into octave band responses by convolving with band-pass ®lters. (e) The software synthesizes four new impulse responses corresponding to four cardioid (front, back, left and right) patterns from O, X and Y impulse responses. (f) The software estimates four directional (front, back, left and right) ``power components'' by multiplying ®gure-of-eight responses and cardioid-directional impulse responses. (g) Finally the software calculates the parameters of early re¯ections such as LC, FBR and LRR from directional impulse responses. All of the above sequences are carried out within about 10 min at one point with the averaging time set four times. This saves much time and provides more detail about the sound ®eld of the auditorium. 4.3. Practical error estimation The error in this method is also estimated practically in an anechoic room. The microphone probe is put in the center of the anechoic room, and three loudspeakers are set in front, to the left and to the right of the microphone probe. When a direct sound from the frontal loud-speaker (with delay 0 ms and amplitude 1.0) and two re¯ection sounds from the left loud-speaker (with delay 30 ms and amplitude 0.3) and the right loudspeaker (with delay 50 ms and amplitude 0.5) are reproduced, the

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Fig. 7. The directional parameters of ``early'' (0±80 ms) re¯ections. The distribution of the directional parameters is shown with the measuring points and the ground plan of the hall.

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Fig. 8. The directional parameters of ``late'' (80 ms Ð RT) re¯ections. The distribution of the directional parameters is shown with the measuring points and the ground plan of the hall.

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measured LC value is ÿ5.75 dB (averaged over the octave bands from 250 Hz to 2 kHz) for the theoretical LC value ÿ5.96 dB. The same estimation is carried out in several conditions (LC=ÿ1.76±17.08 dB). The accuracy, adapted to the LC value of the new method, is about 1.0 dB. The accuracy of the LRR is also about 1.0±2.0 dB, and the accuracy of the FBR is expected to be the same. These values show that all directional parameters can be measured with sucient practical accuracy using the new system. 5. Measurement The hall in which the measurements were carried out was a multi-purpose hall, the arrangement of which could be altered in three ways (for concerts, conventions and exhibitions). The volume was 19,125±32,025 m3 and the reverberation time 1.2±1.7 s. For concerts and conventions, it had 2004 seats, but most of area could be ¯attened for exhibitions. The sound source was located on the center of the stage. The measurements were taken at 12 points for each shape. The distribution of the directional parameters is shown with the measurement points and the ground plan of this hall in Fig. 7. All data in this ®gure are averaged over the octave bands from 250 Hz to 2 kHz. The LC value increases in the rear and side area. In the arrangement for concerts, the di€erence is not so signi®cant because the re¯ector on the stage and the side walls provide sucient early lateral re¯ections. On the other hand, the di€erences are over 10 dB in the arrangement for conventions and exhibitions because the re¯ector is removed. The FBR value decreases at the back. This tends to change inversely to the LC value. The di€erence is more marked in the arrangement for conventions and exhibitions than for concerts. This is also due to the e€ects of the re¯ector and side walls. The LRR value decreases in the right area of the ¯oor, but the di€erence is under +/ÿ5 dB. In Fig. 8, the distribution of the directional parameters of ``late'' re¯ections of this hall is also shown. The integration time is from 80 ms to RT30 instead of the ``early'' 0±80 ms. The maximum and minimum values are shown in Table 1. The di€erences in ``early'' components are always larger than those in ``late'' re¯ections. They are 4.22±10.32 dB for the LC, 2.41±11.38 dB for the FBR and 3.77±5.20 dB for the LRR, compared with the di€erences in ``late'' components of 1.31±2.24 dB for the LC, Table 1 The maximum and minimum values of physical parameters (maximum/minimum in dB) For concerts

LC (dB) FBR (dB) LRR (dB)

For conventions

For exhibitions

Early

Late

Early

Late

Early

Late

ÿ4.33/ÿ8.55 8.33/ 5.92 1.49/ÿ2.28

ÿ3.00/ÿ4.63 4.21/ 1.96 2.39/ 0.00

ÿ4.86/ÿ15.18 14.41/ 5.99 1.94/ÿ3.26

ÿ2.90/ÿ4.21 2.54/ 0.48 2.15/ 1.29

ÿ4.13/ÿ11.24 15.34/ 3.96 2.22/ÿ2.77

ÿ2.44/ÿ4.68 3.32/ 0.81 2.16/ 0.80

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2.06±2.51 dB for the FBR and 0.86±2.39 dB for the LRR. Therefore, the directional parameters of ``early'' re¯ections can be more useful as parameters which re¯ect the di€erences between seats. 6. Conclusion A new method for measuring directional room acoustical parameters is presented. The polar pattern of the microphone becomes narrow compared with the cardioidpattern, and it is close to one side of the ®gure-of-eight pattern. The directional parameters can be measured with sucient practical accuracy by the new method. This method has been used to make measurements in a multi-purpose hall, showing that the directional parameters of early re¯ections are sensitive to room shape and the positions of seats. The new method presented here should be useful for investigating the relationship between spatial impressions and the room acoustical parameters. Acknowledgements The authors would like to thank Dr. Nishi for his encouragement of this research, and Mr. Kitamura of NHK Engineering Service Corp. and Mr. Furukawa of Furukawa Architectural Acoustic Labs. for cooperation when the measurements were made and other helpful discussions. References [1] Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12. [2] Barron M, Marshall AH. Spatial impression due to early lateral re¯ections in concert halls: the derivation of a physical measure. Journal of Sound and Vibration 1981;77:211±32. [3] Morimoto M, Iida K. A new physical measure for psychological evaluation of a sound ®eld: front/ back energy ratio as a measure for envelopment. Journal of Acoustical Society of America 1993;93(4):22282. [4] Thiele R. Richtungsverteilung und Zeitfolge der Schallruckwurfe in Raumen. ACUSTICA 1953;3:291. [5] Mayer E, Kuttru€ H, Roy N. Raumakustische untersuchungen an einem modell der stadthalle in Gottingen. ACUSTICA 1967;19:132. [6] Yamasaki Y, Itow T. Measurement of spatial information in sound ®elds by closely located four point microphone method, Journal of Acoustical Society of Japan (E), 1989;10:2. [7] Flanagan JL. Use of acoustic ®ltering to control the beamwidth of steered microphone arrays. Journal of Acoustical Society of America 1985;78(2):423. [8] Nishi T, Inoue T. Development of multi-beam array microphone for multichannel pickup of sound ®elds. ACUSTICA 1992;76:163±72. [9] Sekiguchi K, Kimura S, Hanyuu T. Analysis of sound ®eld on spacial information using a fourchannel microphone system based on regular tetrahedron peak point method. Applied Acoustics 1992;37:305±23.

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[10] Jordan VL. Acoustical design of concert halls and theaters. Applied Science publishers, 1980. p. 187. [11] Cox TJ, Davis WJ, Lam YW. The sensitivity of listeners to early sound ®eld changes in auditoria. ACUSTICA 1993;79:27±41. [12] Aoshima N. Computer-generated pulse signal applied for sound measurement. Journal of Acoustical Society of America 1981;69(5):1484±8. [13] Tachibana H. Dodecahedral loudspeaker for measuring acoustical characteristics of a room, Arch. Acoust Noise Control 1985;14:64±5.