J. Acoust. Soc. Jpn. (E) 10, 2 (1989)
Measurement of spatial information in sound fieldsMeasurement of spatial information in sound fieldsMeasurement of spatial information in sound fieldsMeasurement of spatial information in sound fieldsMeasurement of spatial information in sound fieldsby closely located four point microphone methodby closely located four point microphone methodby closely located four point microphone methodby closely located four point microphone methodby closely located four point microphone method
Yoshio Yamasaki and Takeshi Itow
Scholl of Scienceand Engineering, Waseda University,3-4-1, Okubo, Shinjuku-ku, Tokyo, 169 Japan
•iReceived 13 December 1988•j
When we estimate a sound field in a room, it is important to grasp the spatial informa-tion, especially of the early reflection periods. In this paper we'll discuss a way to graspthe spatial infornation of sound fields from impulse responses measured at closely locatedfour points, the origin and three points of the same distance (3 •`5cm•jfrom the origin onthe rectangular coordinate axes. From these four impulse responses the coordinatesand powers of virtual image sources are calculated by correlation technique or intensitytechnique. Concert halls, opera theaters and many other sound fields are measured bythis technique. The distributions of virtual image sources and directivity patterns ofsome concert halls are shown.
PACS numrber: 43. 55. Br, 43. 55. Gx, 43. 85. -c
1. INTRODUCTlON1. INTRODUCTlON1. INTRODUCTlON1. INTRODUCTlON1. INTRODUCTlON
•@Reverberation times and sound pressure levels arevery important parameters to evaluate sound fields.But we often get a quite different acoustic im-pression in the sound fields which have about thesame reverberation time and sound pressure level.This kind of difference might come from the dif-frence of spatial information, especially in earlyreflection periods. So it is important to graspspatial informations of sound fields. Many effortshave been done about this problem, for exampleto introduce a microphone which has very sharpdirectivity.  Here, we'll discuss a way to grasp spatial informa-tion of sound fields from impulse responses measuredat clsely located four points; the origin, and threepoints of the same distance (3 •`5cm) from theorigin on the rectangular coordinate axes. Fromsmall differences of these four impulse respomses,we try to estimate the positions and powers of directand reflected sound sources by correlation techniqueor intensity techniquc. It might be called threedimensional triangular surveying.
2. IMPULSE RESPONSE OF2. IMPULSE RESPONSE OF2. IMPULSE RESPONSE OF2. IMPULSE RESPONSE OF2. IMPULSE RESPONSE OF
SOUNDFIELDSSOUNDFIELDSSOUNDFIELDSSOUNDFIELDSSOUNDFIELDS
  An impulse response of a sound field consists ofthe direct sound, discretely reflected sounds anddegenerated number of reflections and representsthe transmission characteristics from a certainsource point to an observation point. We cancalculate output signals for any input signals by theconvolution with the impulse responses, if the soundfield is considered to be a linear and time invariantsystem.  If we measure and keep only one impulse responseof a room, we can calculate afterward not only roomparameters, reverberation time and so on, but alsothe waveform of a music played in the room byconvolving the impuse response with waveform ofdry music, where dry music means a music played inan anechoic chamber. The four point method isdeveloped to keep three more impulse responses toget the spatial information of a sound field.  Usually we measure impulse responses as follows.A loudspeaker, the sound source, is driven by aunit sample pulse whose width is     and amplitude5µs
J. Acoust. Soc. Jpn. (E) 1010101010, 2 (1989)
Fig.1Fig.1Fig.1Fig.1Fig.1  Foour point microphone system.
is 100 V. The output signal of each microphone isdigitized with a 16 bit AD converter whose samplingfrequency is 44.1 kHz or 48 kHz. The digitizedsignals are averaged 32 to 256 times by a personalcomputer to improve the signal to noise ratio. Thenumber of averaging is selected 32 to 256 timesaccording to the background noise level, with suffi-ciently long random intervals to improve the signalto noise ratio not only for random noise but also forperiodical noise.  In some casesm when we hace not enough time tomeasure or the background noise level is very high,we use preudo random noise or rapidly sweptsinusoidal wave  instead of the unit sample pulsesand they are directly recorded to a digital taperecorder.
3. MICROPHONE ARRANGEMENT3. MICROPHONE ARRANGEMENT3. MICROPHONE ARRANGEMENT3. MICROPHONE ARRANGEMENT3. MICROPHONE ARRANGEMENT
  Usually we use a four point microphone systemshown in Fig.1. Four microphones are located atthe origin of a coordinate and the three points onthe rectangular coordinate axes at the same distancefrom the origin. Theoretically four microphonesshould not be placed on the same plane and thedistances of microphones should be sufficientlyshorter than the wacelength of the sound.  Though the shorter the distances of microhonesare the better in theory, actually we must decide thedistance considering the accuracy in the mechanicalset up and the numerical computation. We usethe 8 mm diameter diaphragm electrostatic micro-phones with the distance of 50 mm for ordinary
measurements, in the concert halls or opera houses.The distance is set 33 mm for the measurements insmaller rooms. 3 mm diameter microphones are usedwith 5 mm distance for scale model measurements.
4. CALCULATION OF COORDINATES4. CALCULATION OF COORDINATES4. CALCULATION OF COORDINATES4. CALCULATION OF COORDINATES4. CALCULATION OF COORDINATES
OF VIRTUAL IMAGE SOURCESOF VIRTUAL IMAGE SOURCESOF VIRTUAL IMAGE SOURCESOF VIRTUAL IMAGE SOURCESOF VIRTUAL IMAGE SOURCES
  From impulse responses observed at closelylocated four points we can calculate the coordinatesof the virtual image sources, as follows:  Figure 2 shows the simple ecperiment in anechoicchamber with hard (iron) and soft (iron covered byurethane foam) walls. The local peaks in theimpluse responses represent the traveling distanceof the reflected wave as shown in Fig.2(b). Thesound source corresponding to each local peakshould be on a spherical surface of radius   whosechenter is at the observation point as shown inFig.3, where              , expresses the travelingdistance from each microphone.  The four local peaks make the four spheres. Theintersection of four spheres is the point of thesound source corresponding to the direct sound or thereflected sound. OF course, sound fields are verycomplicated, and we can estimate only the sourcepoints corresponding to the direct sound and afew reflections. As shown in the later part, esti-mated source points corresponding to the reflectionsare considered to be of the degenerated equivalentreflections. So we call them as virtual image sources.  In Fig.2(b),          and    correspond to thedistances between a certain source and each observa-tion point. Then the distances are
where    is the velocity of the sound.  From spherical equations, the coordinates of avirtual image source            are
where   is the distance of microphones.  Figures 2(c)~(f) show the distributions of virtualimage sources prejected to       and         plane.The center of the squares represents the calculatedcoordinates of the virtual image source, and the area
, , , )(o x y zrin i=
ynxnonttt,,znt
lxznynyn
xnxnononc trc tr
c trc tr
),,(nnnY ZX
X −YZX −
Y.YAMASAKI and T.ITOW: FOUR POINT MICROPHONE MEASUREMENT
Fig.2Fig.2Fig.2Fig.2Fig.2  Principle of four point measurement.
(a) Sketch of equipments
  (b) Impuls responses
   (c) projected to X-Z plane (Iron)  (f) projected to X-Z plane (Urethane)
of each square represents tile power of the corre-sponding sourcce. The direct sound is displayedalmost same but the reflections are observed clearlydifferent. That is, the refleted image sources ofsort wall are much weaker and distributed widelybecause of the dinfference or reflectlion character-istics.
4.1 Correlation Technique Here we'll explain the process to calculate thecoordinate of the virtual image sources by correla-tion technique: 1) Four impulse responses are interpolated 256times to keep high accuracy in the following process.
J. Acoust. Soc. Jpn. (E) 1010101010, 2 (1989)
Fig.3Fig.3Fig.3Fig.3Fig.3  Calculation of reflection.
 2) The corresponding reflections are selected byuse of the cross-correlation function. 3) The distance between a virtual image sourceand each observation point is decided from 1). 4) The coordinate of the virtual image sourceis calculated by Eq.(2). We used to interpolate impulse responses 256times to keep high accuracy by main frame com-puters. For the convenience of field measurements,we introduce stand alone system with personalcompulers. The personalcomputer system has notenough speed for such a high rate interpolation. Sowe make some arrangement in softwares, that is tointerpolate not whole impulse responses, but onlywithin durations in which some reflections areexist. And the adaptive processingis also intro-duced as follows:1) The six short time correlation coefficients from   to                             , between thefour impulse responses,                       arecalculaled by the following equation
where             and 2) The    which gives local peak of each correlationcoefficient is searched, and the length ofwhich gives correlation coefficient more than athreshold value (we usually use 0.8) is determined.Let the    which gives local peaks of correlationccefficient be                       and   be
 3) The minimum duration      of    is searched. 4) Duration      is interpolated 16 times, todetermine              precisely. 5) The averaged certain reflection waveform offour impulse responses is calculated and subtracted
from original inmpulse responses. 6) Subsequently the process from 1) to 5) isrepeated.
4.2 Short Time Intensity Technique We explained the calculation of virtual imagesources by correlation technique. Four micro-phones are arranged on the rectangular axes. So wecan calculate intensity vector for three orthogonaldirections. From short time intensiey we can decidethe direction, the distance and the power or a vir-tual image sources by polar coordinate. Strictlyspeaking this is not a image source, but the equiva-lent center of gravity or reflections of some moment.For the sake of convenience, we also call them vir-tual image sources. By intensity technique we can easily calculatevirtual image sources within limited frequecybands. The process is as follows: 1) The impulse response is filtered through aband-pass filter. 2) A part of the impulse response is cut out by ashort time window or certain duration. We usuallyuse 10 ms rectangular windows. 3) The short time intensity vectors are calculatedwith the outputs of three pairs               ofmicrophones, using the imaginary part of crossspectrum. 4) The coordinate of a virtual image source isdetermined by short time intensity vector. 5) The window is shifted to the next priod. 6) The process from 2) to 5) is subsequentlyrepeated.
5. DEVELOPMENT OF VIRTUAL5. DEVELOPMENT OF VIRTUAL5. DEVELOPMENT OF VIRTUAL5. DEVELOPMENT OF VIRTUAL5. DEVELOPMENT OF VIRTUALIMAGE SOURCESIMAGE SOURCESIMAGE SOURCESIMAGE SOURCESIMAGE SOURCES
5.1 Distribution of Virtual Image Sources  Figure 4(a) shows impulse responses ofMusikvereinssaal and Munchen Philharmonie Hall, Fig.4(b) shows distributions of the virtual image sourcesprojected to three planes calculated by the correla-tion technique. The center of the circle representsthe estimated points of the virtual image source,and the area of each circle represents the power ofthe corresponding source. The cross point of thetwo orthogonal lines is the observation point, andthe distance between the progonal sound source andthe obsercation point is 12m. The outlines of theconcert hall are also shown.
atxzyzxyozoyoxaSSSSSSt,,,,,+ ∆,( ),( ),( ),0 ( ),h th th tthzyx
,( ))( )(
)(( ))(1/ 222dth tth
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o x y zi= , , ,x y zj= , ,τ∆
τ,,,,,,xzyzxyozoyoxττττττ∆∆ox ,.,,xzoy∆∆L
∆min,,,Lox ∆oy∆
xzoyoxτττ,,,L
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Y.YAMASAKI and T.ITOW: FOUR POINT MICROPHONE MEASUREMENT
Fig.4  Impulse responses and distribution of virtual image sources (Musikvereinssaal andMunchen Philharmonie.)
 (a) Musikvereinssaal, Wien(b) Munchen Philharmonie
5.2 Time Divided Distribution  Time divided distributions of virtual image sourcescan be also displayed. Figure 5(a) shows the imagesources in the first 50ms from the direct sound, (b)shows those between 50ms and 100ms, (c) showsthose after 100ms.
5.3 Distribution of Limited Space  We can also display distribution of the limitedspace. For example the space is divided to threesections by two planes which are paralleled to floorplane and 10ms above from the observation point.
FIgure 6 shows the virtual image sources projectedto        (floor) plane of above 10m (a), from -10mto +10m (b) and below -10m (c).
5.4 Directivity Patterns (Hedgehog Patterns)  We can calculate directivity patterns by observingthree dimensional distributions of virtual imagesources through the supposed microphone withvertical open angle      degrees as shown in Fig.7.Figure 8 shows directivity patterns, the total powerof virtual image sources with horizontal open angle1, 10 and 30 degrees, vertical open angle 45 degrees,
J. Acoust. Soc. Jpn. (E) 1010101010, 2 (1989)
Fig.5Fig.5Fig.5Fig.5Fig.5  TIme divided distribution (Musik-vereinsssaal). (a) from 0 to 50ms, (b)from 50 to 100ms, (c) after 100ms.
Fig.6Fig.6Fig.6Fig.6Fig.6  Distribution of Limited space (Musik-vereinssaal). (a) above 10m, (b) from-10m to 10m, (c) below -10m.
Fig.7Fig.7Fig.7Fig.7Fig.7  Supposed microphone for calcula-tion of directivity pattern.
and 1 division represents 10 dB.
5.5 Frequency Band Limited Distribution  Figure 9 shows distribution of frequency bandlimited virtual image sources of Musikvereinssaaland Munchen Philharmonie calculated by the intensitytechnique.
5.6 Reconstruction of Impulse Responses  Figure 10 shows impulse responses of Musikverein-ssaal, upper one is original and lower one is recon-structed from calculated virtual image sources. Re-constructed one is thinner than the original one, butit represents well the characteristics of original
Y.YAMASAKI and T.ITOW: FOUR POINT MICROPHONE MEASUREMENT
Fig.8Fig.8Fig.8Fig.8Fig.8  Directivity patterns (Musikvereinssaal).
one especially in early period. So this method can beused for our first aim, to frasp spatial informationof sound fields in early reflection period.  From virtual image sources, we can reconstruct notonly the impulse resoinse of the observation point,but also the impulse respoinses of the point near theobservation point. The impulse responses from spe-cial direction can also be calculated.
6.  CONCLUSION6.  CONCLUSION6.  CONCLUSION6.  CONCLUSION6.  CONCLUSION
  In this paper we discuss the way to grasp the
spatial information in a sound field by a four pointmicrophone method.  FIrst, the principle of this method and the simpleecperiment in anechoic chamber are shown. Thenthe some measurements in actual sound fields areshown, and the development of virtual image sourcesare discussed.  Figure 11 shoes the distribution of virtual imagesources projected to       (floor) plane of threedifferent kinds of sound fields, a living room, aconcert hall (Boston Symohony Hall) and a cathedral
J. Acoust. Soc. Jpn. (E) 1010101010, 2 (1989)
Fig.9Fig.9Fig.9Fig.9Fig.9  Distribution of band limited virtual image sources (Musikvereinssaal and MunchenPhilharmonie).
Y.YAMASAKI and T.ITOW: FOUR POINT MICROPHONE MEASUREMENT
Fig.10Fig.10Fig.10Fig.10Fig.10  Original and re-constructed impulse responses.
Fig.11Fig.11Fig.11Fig.11Fig.11  Impulse responses, distribution of virtual image sources and directivity patterns ofthree different kinds of sound fields.
(Munster in Freiberg). Impulse responses and thedirectivity patterns of floor plane with 1 degreeopen angle are also shown. From the projectedvirtual image sources shown in Figs.4 and 11, ordirectivity patterns shown in FIgs.8 and 11, we caneasily grasp the spatial informations through eyes.
Such as, Musikvereinssaal has very rich side reflec-tions compared to Munchen Philharmonie. And the formerhas rich distributions from bottom, may be floormaterial of this hall is much harder.  We have measured many concert halls and operatheaters in Europe, the United States and Japan.2−5)
J. Acoust. Soc. Jpn. (E) 1010101010, 2 (1989)
Recently we introduce this technique to scale modelmeasurements, too. We also use these data bases toestimate the sound fields  or to feed them bact to theacoustic design.
ACKNOWLEDGMENTSACKNOWLEDGMENTSACKNOWLEDGMENTSACKNOWLEDGMENTSACKNOWLEDGMENTS
  This method has been developed in the acousticlaboratory of Waseda University for these 12 years.The authors would like to acknowledge for contribu-tion of many graduates, especially Shigeru Yamasuda,Yasushi Hatta, Keiji Kogure, Hiroyuki Saito, OsamuEbina, Kenichiro Yasukawa, Kenji Endoh, Shiro Ise,Nobumasa Seiyama, Toshikazu Okada, KazuhikoTakabayashi and Yunnghee Gheem.
REFFERENCESREFFERENCESREFFERENCESREFFERENCESREFFERENCES
1) N.Aoshima, •gCOmputer-generated pulse signal   applied for sound measurement,•h J.Acoust.Soc.   Am. 69, 1484-1488 (1981).
2) Y.Yamasaki, S.Yamasuda, H.Saito, K.Yasukawa,and T.Itow, •gAn application of digital techniquesto obtain the spatial information of a room,•h Rep.U.S.Jpn. Jt. Meet. BBB6 (1978).3) K.Endoh, T.Horikoshi, Y.Yamasaki, and T.Itow, •gGrasp and estimation of spatial informationmethod,•h Proc. ICASSP 86, 909-912 (1986).4) Y.Yamasaki, H.Tachibana, M.Morimoto, Y.Hirasawa, and Z.Maekawa, •gSurvey on theacoustics of concert halls in European countries(The2nd Report)-Measured results by four-pointmicrohopne method-,•h J.Acoust.Soc.Jpn.(J)43, 277-285 (1987) (in Japanese).5) H.Tachibana, Y.Yamasaki, M.Morimoto, Y.Hirasawa, Z.Maekawa, and C.Posse;t, •gAcousticsurvey of auditoriums in Europe and Japan,•h J.Acoust.Soc.Jpn. (E), 10, 73-85 (1989).6) H.Yanagawa, Y.Yamasaki, and T.Itow, •gEffectof transient signal length on cross-correlationfunctions in a room,•h J.Acoust.Soc.Am. 84, 1728-1733 (1988).