3D Microphone Array

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Audio Engineering Society

Convention PaperPresented at the 112th Convention

2002 May 1013 Munich, Germany

This convention paper has been reproduced from the authors advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org . All rights reserved. Reproduction of this paper, or any portion thereof, is

not permitted without direct permission from the Journal of the Audio Engineering Society .

Applications of a 3-D Microphone ArrayJuha Merimaa

Helsinki University of Technology, Lab. of Acoustics and Audio Signal Processing, P.O.Box 3000, FIN-02015, HUT, Finland

Correspondence should be addressed to Juha Merimaa ( [email protected] )

ABSTRACT

Soundeld inside an enclosed space depends in a complex way upon interactions between emitted sound waves anddifferent reecting, diffracting, and scattering surfaces. 3-D microphone arrays provide tools for investigating andrecording these interactions. This paper discusses several existing array techniques introducing a variety of applicationtargets for the HUT microphone probe. Applications include directional measurement, analysis, and visualizationof room responses, estimation of room parameters and analysis of source and surface positions. In a dynamic casethe probe can be utilized in source tracking and beam steering, as well as in tracking its own position. Furthermore,the probe can be used to simulate some microphone arrays commonly used in surround sound recording. In eachapplication case both general theory and its relation to the HUT probe is discussed.

INTRODUCTIONIn all practical situation soundeld inside an enclosed spaceconsists of acoustical waves propagating in several differentdirections. Sound waves emitted by a source are reected,diffracted, and scattered by different obstacles including thewalls of the enclosure. This results in a complex eld, theproperties of which cannot be comprehensively captured inone-dimensional signals or parameters.

Different practitioners have different viewpoints into spatialsound. Researchers and acoustical engineers often want tomeasure a response to a given stimulus in a room, in order

to gain information about the reasons why the room soundslike it does. The motivation for this may be an attempt tochange the acoustics, or a pure scientic interest in the un-derlying phenomena, including perception of spatial sound. Arecording engineer, on the other hand, may want to capture aperformance in a room so that an illusion of the room can belater reproduced somewhere else. Another related problem isselective recording of certain sound sources. Third distinctarea of interest is acoustical orientation, i.e., localization of sound sources, reecting obstacles and surfaces, or the re-ceiver itself based on received sound signals. Of course, there

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MERIMAA APPLICATIONS OF A 3-D MICROPHONE ARRAY

Fig. 1: The HUT 3-D microphone probe.

are also intersections between these viewpoints.

This paper describes applications of a 3-D microphone arrayin all the previously mentioned tasks. The HUT microphoneprobe consists of 12 miniature electret microphone capsulesarranged as two concentric pairs in each of x-, y-, and z-coordinate axes. The inner pairs are set with a spacing of 10mm and the outer pairs with a spacing of 100 mm between thecapsules. The probe was originally designed for measurementpurposes but has proven useful in other applications as well.A picture of the probe is shown in Fig. 1. Related hardwareand software are described in [1] and [2].

The paper is divided into three parts. The rst part discussesdirectional measurement and analysis of room responses. Sec-ond part presents some possibilities of using the probe insound recording. Finally, the third part introduces sourcelocalization techniques applicable both in measurement pur-poses and in acoustical orientation.

ROOM RESPONSE MEASUREMENTSMeasurement of room responses and analysis of related at-tributes is a common task in audio and acoustics. Most oftenan omnidirectional response to a preferably omnidirectional

stimulus is acquired. This is sufficient for calculation of sev-eral room-acoustical parameters. However, single omnidirec-tional responses and standard parameters provide only lim-ited information about the actual acoustics of the room andits perceptual properties.

Microphone array techniques utlilized in room response mea-surements can be roughly divided into two categories. Inthe rst category large arrays spanning a signicant distance,area, or volume in the room are utilized. This gives a repre-sentation of the evolving soundeld as a function of spatialposition. Application of a long line array in this purpose

has been described in [3]. In the second category small arrayssuch as the HUT microphone probe are used to give a listenercentered view of the directional soundeld. The following dis-cussion concentrates on methods in the latter category.

Directional sound pressure componentsIdeal omnidirectional microphones are sensitive to sound pres-sure, which as a scalar quantity does not include any direc-tional information. Systems with varying directional sensitiv-ity can be formed by appropriately combining the signals of two or more closely spaced omnidirectional microphones. Anattractive feature of using an array of omnidirectional micro-phones in place of directional microphones is the possibilityto vary and steer the directivity patterns later in the postpro-cessing phase.

First-order differential directivity patterns can be easily cre-ated using the signals of a closely spaced pair of microphones.This kind of beamforming methods are analogous to the con-struction of microphones with built-in directionality [4, 5].Basically, all that is needed is some equalization and delay,and a weighted summation of the resulting signals. An idealdipole has a directivity pattern of the form

E () = cos( ) (1)

where is the angle of arrival of a plane wave related to theline connecting the pair of microphones. This kind of a pat-tern is constructed from the equalized difference of the signalsof the microphones. A cardioid pattern, on the other hand,is based on a difference where one of the signals is delayedby the time corresponding to the propagation of sound overthe distance between the microphones. Another way of form-ing a cardioid is to sum two signals with omnidirectional anddipole directivity patterns. More generally, any rst-orderdifferential pattern can be formed as a weighted sum of anomnidirectional pattern and a dipole pattern resulting in thedirectivity

E () = + (1 ) cos( ) (2)Differential directivity patterns with some common areshown in Fig. 2.

A simple steering method for rst-order differential patternshas been patented by Elko [6]. His method is based on steer-ing a dipole pattern, after which any rst-order pattern canbe created as a combination with an omnidirectional signal asdescribed. In the case of the HUT microphone probe dipolesin x-, y-, and z-directions can be readily formed from corre-sponding microphone pairs. A signal of a steered dipole canthen be written in the form

E (, ) = cos( ) sin( )E x + sin( ) sin( )E y + cos( )E z (3)

where is the azimuth angle and is the elevation angle of the resulting dipole pattern, and E x , E y , and E z are signalswith dipole patterns facing at the directions of x-, y-, and

z-axis, respectively.The resolution provided by rst-order differential directivitypatterns may not always be optimal for measurement pur-poses. Okubo et al. [7] have proposed a product of dipole andcardioid signals in order to construct a unidirectional directiv-ity pattern with more selectivity than the rst-order cardioid.The resulting pattern is shown in Fig. 3. For broadband sig-nals this method is, of course, applicable in the frequencydomain only, since a time domain multiplication would resultin harmonics at sum and difference frequencies of original sig-nal components. Okubo et al were using an array with single

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Fig. 2: Polar plots of the logarithmic magnitude responses of rst-order differential directivity patterns with some typical in Eq (2).

concentric pairs of omnidirectional microphones on horizontal(x- and y-) coordinate axis, complemented with a microphonein the middle of the array.

The difference of the signals of a pair of microphones ap-proximates the gradient of the soundeld at low frequencies.The upper frequency limit is constrained by the distance be-tween the microphones. At frequencies where the wavelengthof sound is comparable to the microphone spacing, the ap-proximation of gradient is no longer valid and the directivitypattern is distorted. The lower limit, on the other hand, isdened by the phase errors and signal-to-noise ratio of themeasurement system. Furthermore, the so called proximityeffect causes the magnitude response of a differential systemto depend on the distance of a sound source located close tothe microphones [4]. In the HUT microphone probe thesefrequency range problems have been alleviated by positioningtwo sets of microphones at different distances from the center,allowing thus combined operation on two frequency scales.

Apart from differential techniques, a common method forbeamforming is summation of several microphone signals de-layed so that they are in phase for sound waves arriving fromthe desired direction. A problem related to this kind of meth-ods is changing directivity as a function of frequency. Thenarrowing of the beam with increasing frequency can be pre-

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Fig. 3: A polar plot of the logarithmic magnitude responseof the directivity pattern proposed by Okubo et al [7].

vented by frequency dependent shading of the outer elementsin an array [8, 9]. Arrays with non-uniform spacing betweenmicrophones have also been used [10]. However, delay-and-sum beamforming at low frequencies requires the size of anarray to be comparable to the wavelength of sound, while thespacing between the microphones used at high frequenciesneeds be comparable to the wavelength at those frequenciesin order to avoid spatial aliasing. For a small array, suchas the HUT microphone probe, differential methods providethus better results for wideband beamforming. If the HUTprobe were to be used as a delay-and-sum beamformer, itsgeometry could be utilized either as line or plane arrays, oras a sparsely sampled spherical shell or volume array [11, 12].

Separation of measured impulse responses into directionalcomponents allows isolated investigation of reections anddiffraction caused by objects in a chosen direction as seenfrom the listening position. This may sometimes be useful,but in general separate treatment of different directions re-sults in a vast amount of data that is hard to interpret. Thatis why patterns with higher directivity have not been foundvery practical in measurement applications. On the contrary,methods for more compact representation of data have beenexplored. However, Broadhurst [13] has described the designof a sparse volumetric array having a beamwidth of 32 foracoustical measurements. Unfortunately he does not discussthe actual measurements and their interpretation in his paper.Some higher order beamforming methods are also applicablewith the HUT microphone and will be discussed in this paperin connection with acoustic communications applications andsource localization.

Sound intensitySound intensity describes the propagation of energy in a

soundeld. Being a vector quantity, it naturally includes a di-rectional aspect. Measured sound intensity data complementsnicely the pressure-related impulse responses in characteriza-tion of a directional soundeld. Especially the differencesbetween sound pressure and intensity elds may be of inter-est. For example, in a completely diffuse soundeld, intensityshould be zero irrespective of the sound pressure level.

Intensity is dened as the product of sound pressure andparticle velocity. In a standard intensity measurement tech-nique the pressure signals p1 (t ) and p2 (t ) of a pair of closelyplaced omnidirectional microphones are used to approximate



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the pressure and velocity components in a point halfway be-tween the microphones. With these signals the instantaneousintensity in the direction of a line connecting the two micro-phones can be approximated with

I (t ) 120 d

[ p1 (t ) + p2 (t )]

t

[ p1 ( ) p2 ( )] d (4)

where 0 is the mean density of air and d is the distancebetween the microphones [14]. A 3-D intensity vector can bedetermined using three concentric pairs of microphones in thedirections of x-, y-, and z-coordinate axis, such as in the HUTmicrophone probe.

Sound intensity can be divided into active and reactive com-ponents. The active component describes the net transport of sound energy and can be calculated as the average of instan-taneous intensity. Frequency distribution of active intensitycan also be determined with an FFT-based method from theimaginary part of the cross-spectral density G p 1 p 2 of the mi-crophone signals [14, 15]

I () j

0 d Im {G p1 p 2 ()} (5)

where is the angular frequency, j is the imaginary unit, andG p 1 p 2 is given by

G p 1 p 2 () = 2 P 1 ()P 2 () (6)

where denotes the complex conjugate and P 1 () and P 2 ()are the Fourier transforms of the microphone signals p1 (t ) and p2 (t ), respectively.

The nite difference approximations of sound pressure andparticle velocity in the point halfway between the micro-phones cause frequency dependent systematic error to the ap-proximation. The actual error depends on the acoustical eldbeing measured [14]. Chung [16] has proposed a practicalupper limit of

kd = 1 f L =c

2d (7)where k is the wave number, f L is the limiting frequency andc is the speed of sound. The practical lower frequency limit,on the other hand, depends on the phase errors of the mea-surement system. In the HUT microphone probe concentricmicrophone pairs with two different spacings can once againbe used to extend the frequency range. With a larger arrayhaving microphones outside the coordinate axis, a methodproposed by Kuttruff [17] could also be utilized in order tofurther reduce the approximation errors.

Visualization of directional room responsesAs mentioned earlier, directional processing of room responsesresults in a large amount of data that is difficult to interpret.Examining several gures of directional sound pressure andintensity components is not very informative. A simple visu-

alization method for directional room responses was proposedin [18]. The method is a combination of two overlaid plots.Active intensity is represented as vectors (quiver plot) laid ontop of a sound pressure related spectrogram. Both quantitiesare analyzed with same time-frequency resolution. One com-bination plot illustrates horizontal information and anotherone elevation information in the median plane. In the orig-inal paper both uniform and auditory frequency resolutionswere applied.

An example of the visualization method is shown in Fig. 4.The plot clearly shows the direct sound followed by discrete

reections from the oor, the ceiling, and the front wall of theroom. After these the density of reections gets higher andthe chosen time-frequency resolution cannot distinguish singlewideband reections. In a larger room the rst reections are

sparser in time and interesting phenomena can still be seenmuch later in the responses.

SOUND RECORDINGIn conventional studio recording applications microphone ar-rays may not provide much added value. Typically, a record-ing engineer can choose the microphones he likes and set themthe way he likes. Arrays could, of course, be used to simu-late directional microphones, but there is no point in usinga number of expensive studio quality microphones to replacesingle devices that are readily available. However, in naturalstereo and surround sound recording, as well as in telecon-ferencing applications, microphone arrays have proven useful.The following discussion concentrates on surround sound andteleconferencing arrays. For a review of the fairly well estab-lished stereo recording techniques see [19].

Surround soundSeveral current and past surround sound reproduction sys-tems are discussed in a review by Steinke [20]. Correspond-ing multi-channel recording techniques can be roughly dividedinto two categories similar to the measurement arrays. In therst category several microphones are placed in different loca-tions in a room or a concert hall. Typically some of them arelocated close to sound sources to get the direct sound, whileothers are used to capture the reverberation and spatiousnessfrom a distance. Often more ambience is added with arti-cial reverberators. The resulting signals are then processedand mixed down into a set of channels for reproduction witha specic loudspeaker setup. This kind of a recording tech-niques do not necessarily require any microphone arrays. If the acoustics of a hall is tried to reproduce as naturally aspossible, a small number of microphones with a denite place-ment related to each other is, however, often used as a mainarray. Principles of this kind of recording techniques and somecommon geometries for main arrays for 5.1 reproduction, arediscussed in [21].

Recording arrays in the second category try to capture theauthentic soundeld in a single position in a room. Thesearrays can be further divided into coincident and spaced se-tups, where coincident arrays aim for recording the soundeldin a single point of space while in spaced arrays microphonesare set with small distances between them. Lipschitz [19] stillcategorizes spaced arrays into quasi-coincident and spaced se-tups based on the distances between microphones. In thistext, however, both quasi-coincident and spaced arrays arereferred to as spaced.

Coincident recording arraysThe earliest surround sound reproduction systems were socalled quadraphonic setups where four loudspeakers wereplaced in corners of a rectangle with two speakers in frontof and two speakers behind the listener. (The term quadra-phonics also refers to matrixing of four discrete mono repro-duction channels into a stereo signal [20, 22, 23].) Design of a single quadraphonic microphone consisting of four coinci-dent cardioids aligned in the directions of the loudspeakersis described in [24]. A quadraphonic loudspeaker setup can-not, however, create an illusion of sound sources on the sidesof the listener because of the known incapability to createstable phantom sources between speakers positioned in front



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Fig. 4: Visualization of the directional room responses measured from the listening room of HUT Acoustics laboratory, analyzedwith a uniform time-frequency resolution. The direct sound arrives in about 7 ms from a front left direction in the horizontolplane. The next events are reections from the oor and from the ceiling and can be seen to propagate to the same directionin the horizontal plane. In about 12 ms these there can be seen some more diffuse reections from the diffracting constructionson the left side wall followed by a clear discrete reection from the front wall of the room in about 15 ms. After 20 ms no clearwideband reections can be seen anymore.

of and behind the listener [25]. Also the insufficient direc-tional resolution provided by cardioid microphones causes arecorded sound source to spread into several or all loudspeak-ers in reproduction.

Ambisonics [26, 27, 28] is a generalized 3-D system approachto surround sound. The method is based on reconstruction of soundeld with spherical harmonic functions. In theory, func-tions up to any order could be used [28]. However, only rst-and second order systems have been found to be practical. Inthe so called B-format of rst-order ambisonics the soundeldis divided into an omnidirectional component W (zeroth-orderspherical harmonic) and three dipole components X , Y , andZ in the directions of corresponding cartesian coordinate axis(three linearly independent rst-order spherical harmonics).The signal P (, ) to be reproduced by a loudspeaker in anydirection dened by the azimuth angle and the elevation

angle , can then be written in the formP (, ) = W + 3[cos( ) sin( )X + sin( ) sin( )Y + cos( )Z ]

(8)where it is assumed that the level of W equals the level of thedipole signals in the direction of their maximum gain [28].

The gain coefficient 3 in Eq (8) compensates for the lowerpickup energy of dipoles in a diffuse eld. The resultingsum corresponds to a signal recorded from a soundeld witha hypercardioid microphone pointing in the direction of theloudspeaker used for reproduction. This gives maximal direc-

tional discrimination that is available with rst-order direc-tivity patterns. However, the large rear-lobe of a hypercar-dioid causes a recorded signal to be reproduced in oppositephase from loudspeakers in opposite directions. Dependingon loudspeaker conguration less resolution may sometimesgive better sounding results, and can be achieved by reducingthe gain factor [28]. In [26, 29, 30] a coefficient of 2 has beenutilized resulting in a pattern close to supercardioid.

Typically rst-order ambisonics is recorded with a soundeldmicrophone constructed of four coincident cardioid capsulesmounted in the form of a tetrahedron [31, 32]. A cardioidpattern consists of zeroth- and rst-order spherical harmon-ics, and the B-format signals can thus be constructed fromthe cardioids with simple linear algebra. The easiest way touse the HUT microphone probe for ambisonics recordings is,however, to directly extract the omnidirectional and dipole

signals needed in the B-format.A second-order ambisonics system can be formed by addingve microphone channels with linearly independent second-order spherical harmonic (clover-leaf) pickup patterns to arst-order system. The second-order patterns are illustratedin Fig. 5. All the signals needed for construction of these pat-terns, as well as the rst-order patterns, can be obtained usingan array of twelwe small cardioid capsules mounted to forma regular dodecahedron. In this case, the unavoidable non-coincidence of the microphones is taken advantage of by cre-ating the second-order patterns by applying differential tech-



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xy xz yz x 2 y 2 3z2 1

Fig. 5: Second order spherical harmonic functions.

niques to the cardioid signals [28]. The required second-orderpatterns can also be formed for a limited frequency range withthe HUT microphone probe. However, steering them to cor-rect directions related to each other is not possible and thus

second-order abisonics cannot be recorded. Construction of second-order differential patterns with the probe is discussedin more detail in the section of acoustic communications ap-plications in this paper.

The absolute minimum number of loudspeakers for ambisonicreproduction is dened by the number of encoded channels,i.e., for rst-order ambisonics the minimum is 4 and forsecond-order 9. More than that are needed to fully reproduceall the encoded information about the spatial distribution of sound energy around a listener. However, in ambisonics thedirectional resolution is naturally limited by the order of thespherical harmonic reconstruction and thus adding more loud-speakers will not sharpen the images after a certain limit [28].

The focus of phantom images resulting from several coincidentmulti-channel recording and panning techniques in a 2-D re-production system has been compared by Martin et al [29].In their tests with an 8-speaker setup, second-order ambison-ics was able to produce very focused images in all directions.First-order ambisonics was less focused and the effect of re-production of signals with opposite phase on the sides of a lis-tener was apparent. The most blurred images were producedby a panning method simulating recordings with 8 cardioidmicrophones. An interesting comparison of simulated direc-tional localization cues produced by different recording andreproduction methods has also been presented by Pulkki [30].

Spaced recording arraysRecordings with an array of coincident microphones cap-ture only localization cues that are recreated in reproductionwith some form of amplitude panning between loudspeakers.Theile [21] has argued that microphones with a wider spac-ing are able to produce more natural spatial impression due

to their inherent inter-channel temporal differences betweenrecorded channels. However, the perceived images of discretesound sources will usually be more ambiguous [19, 30]. Thisscheme may also lead to severe colorization due to comb l-tering, if signals are mixed down with a simple summation forreproduction with a system with less channels.

Implementation of several spaced surround sound recordingarrays has been described in the literature. Johnston andLam [33] have reported experiments with a 3-D array of sevendirectional microphones. In their array, ve hypercardioid mi-crophones were placed on a circle in the horizontal plane and

two microphones with more directivity were facing up anddown. Special arrays incorporating a diffracting sphere anda dummy head have been described in [34] and [35], respec-tively. This kind of constructions are not possible with the

HUT microphone probe, although coincident patterns similarto the ones used by Johnston and Lam could be formed.

Williams and Le D u [36] have developed an interesting tech-nique for construction of 2-D recording arrays from cardioidmicrophones. To take full advantage of their method the po-sitions and orientations of the recording microphones need tobe adjustable, but some principles can also be applied to anarray of coincident directional microphones. The method isbased on manipulation of so called coverage angles of pairsof directional microphones. A coverage angle determines thelimits for directional angles of sound sources, as seen by themicrophones, that can be naturally reproduced with a pair of loudspeakers. If a source gets outside the coverage angle itwill be localized into one loudspeaker only. The angle dependson the distance and the angle between microphones forming apair and it can be offset (rotated) by non-symmetrical move-ment of the microphones, or by introducing delay or gain toone of the microphone signals. The rotation can be seen as aform of time-intensity trading used to adjust the localizationof a phantom source created from a real source in a deneddirection. The trading, of course, results in conicting ILDand ITD cues in reproduction, but within reasonable limitsthe coverage angles can be adjusted.

The idea of the method of Williams and Le D u is to manip-ulate coverage angles of pairs of adjacent microphones in anarray such that they nally cover 360 with no overlap. Therecorded and manipulated signals of microphones are thenplayed back with corresponding loudspeakers. The numberof microphones and loudspeakers must be the same but theirdirections can differ. If the angle between a pair of loudspeak-ers is different from the coverage angle of the correspondingpair of microphones, the soundscape inside the coverage anglewill be stretched or compressed in playback, accordingly.

Since in the case of the HUT microphone probe, adjustmentof coverage angles by changing distances between pairs of di-rectional microphones is not possible, the usability of the al-gorithm is limited. A new degree of freedom can, however,be introduced by allowing small changes in the directivity of a simulated microphone. This will once again lead to differ-ent distortion of the reproduced surrounding sound eld. Amore formal analysis of the different warpings created by thismethod, with or without a possibility to adjust the directivity



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Fig. 6: Second order toroidal directivity pattern.

patterns, would require further testing.

Acoustic communications applicationsFor teleconferencing applications several special microphonesand microphone arrays have been developed. Automatic mi-crophone steering is one possibility for enhancing the pickupof a single speaker. Steering of rst-order differential direc-tivity patterns was already discussed in measurement appli-cations and source localization methods will be introduced inthe following section. A different approach is taken in systemswith special directivity patterns. One common constructionis a toroidal pattern (Fig. 6). The idea is that a toroidalmicrophone is placed on a table where it effectively picks upthe speech of people sitting around the table while rejectingthe sound from an overhead speaker.

A rst-order toroid having a dipole pickup pattern in anyvertical plane can be constructed by summing the signals of two orthogonal coincident horizontal dipoles in quadraturephase [4]. This can be easily realized with the HUT micro-phone probe by forming two dipole signals and using a Hilberttransformer [38] to rotate the phase of one of them by 90 .Second-order toroids, on the other hand, can be directly cre-ated by summing the signals of two orthogonal coincidentsecond-order dipoles.

An implementation of a second-order toroidal microphonesystem with four closely spaced rst-order dipoles is describedby Sessler et al [39, 40]. The same method can be applied tothe HUT microphone probe as follows. The placement of theomnidirectional microphones in the horizontal plane of theprobe is illustrated in Fig. 7. Four closely spaced rst-orderdipole patterns can be formed as the difference signals of pairs(1 , 5), (2 , 6), (3 , 7), and (4 , 8). Second-order dipoles now re-sult from the summation of dipoles (1 , 5) with (3 , 7), and (2 , 6)with (4 , 8). A toroidal pattern is, thus, created as the sum of all the four dipole signals. Unofortunately this kind of use of second-order techniques prevents the extension of frequencyrange by combined use of two pairs of microphes with differ-ent spacings. Moreover, problems with signal-to-noise ratioand proximity effect get more severe with higher directivity.Thus, either frequency range must be limited or directivityneeds to be compromised when using the probe as a toroidalmicrophone.

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Another useful feature in microphone systems designed forcommunications applications is higher order unidirectional-ity. More directivity is especially needed in noisy environ-ments in order to pick up as little background noise as pos-sible. Several different second-order unidirectional patternscan be constructed by differential techniques based on rst-order differential signals. Design of a unidirectional patternas a cardioid formed from two dipole signals is described in[41] and similar patterns can also be created with the HUT

microphone probe. Elko et al have also proposed an image-derived method for constructing second-order unidirectionalor toroidal directivity patterns with an omnidirectional micro-phone, a rst-order dipole microphone and a reecting tabletop or a wall [37].

An application with a varying directivity pattern has beenintroduced by Ishigaki et al. In [42] they describe an electron-ically zoomable microphone system to be used with a videocamera based on mixing and ltering three cardioid signals.Another system with varying directivity as a function of fre-quency is described by Woszczyk [43]. He describes a systemwhere directivity is increased for lower frequencies in order topick up less reverberation when recording far from a soundsource. The changing directivity is implemented with simplefrequency dependent ltering of signals before using them toform a differential directivity pattern. For example, a dipole

can be turned into an omnidirectional pattern at a chosen fre-quency by ltering another one of the original omnidirectionalsignals to zero.

SOURCE LOCALIZATIONSource localization has been studied extensively in connec-tion with sonar applications, underwater acoustics, and au-tomatic tracking of speakers in conference rooms. Antennaliterature is also a good source for information on this topic.A comprehensive review of existing localization techniques isfar beyond the scope of this paper. Instead, a brief overview



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of the methodology is given and the techniques based on timedelay estimation are introduced in more detail. Finally, useof source localization in measurement and recording applica-tions is discussed.

Localization problems arise in active and passive applications.In active applications the same system controls both a soundsource and a receiver. This gives some distinct advantages.First, the signal emitted by the source can be chosen and isalways precisely known. Furthermore, the whole system canoften be designed to operate at certain limited bandwidth,which alleviates problems related to beamforming and designof the receiving array. On the other hand, in a general caseof passive localization there is no a priori knowledge of thesound source. The goal of passive localization is usually tond the position or the direction of a sound source or severalsources, while active systems aim at nding objects reectingsound waves. The following discussion concentrates on meth-ods useful in both active and passive applications operatingat audio frequencies.

Array-based localization procedures can be loosely dividedinto three categories [44]. In the rst category source is lo-calized by maximizing the output of a steerable beamformer.One system for automatic search and recording of a singlespeaker in a larger room has been introduced by Flanaganet al [45]. Their system utilized a larger 2-D array of micro-phones with delay-and-sum beamforming, but a correspond-ing scheme can be implemented with the HUT microphoneprobe using steerable rst-order differential directivity pat-terns. In the implementation of Flanagan et al simultaneousbeams were utilized, one of which was used for recording andanother one for scanning the room for a new speaker.

Statistical performance of beam steering based source local-ization has been discussed in [46] and is compared to that of the cross-correlation based time delay estimation localizationscheme (see the next section in this paper) in [47]. Presence of several concurrent sound sources is one of the major problemsin this kind of localization. Flanagan et al ended up imple-menting a speech detection algorithm to distinguish betweenspeakers and acoustical background noise. Wax and Kailath[48] have extended the methodology to simultaneous localiza-tion of multiple sound sources, but their technique requiresprior knowledge or the power spectra of all sound sources.

In the second category, methods of high-resolution spectralanalysis are utilized in beamforming. Most methods in thisgroup are originally designed for narrowband signals [44].Extensions to wideband localization have been introducedbased on analysis of signal components at several subbandsboth independently and interdependently. A coherent signal-subspace method being able to separate several sound sourceshas been introduced by Wang and Kaveh [49], and a relatedmethod exploiting higher order statistics has been recentlyproposed by Bourennane and Bendjama [50].

Time delay estimation based methodsThe localization methods in the rst two categories require asearch over the potential directions of sound sources. Withtime delay estimate (TDE) based methods searching can beavoided. In these methods the relative delays between mi-crophones in an array are rst calculated. This is typicallydone by nding the maximum of a measure of similarity be-tween the signals of each pair of microphones as a function of their relative time lag. Delays are then used to determine thelocation or direction of a sound source.

A common measure of similarity is the generalized cross-correlation (GCC) function [51]. GCC is dened as the in-verse Fourier transform of the weighted cross-spectrum of twomicrophone signals

R GCC ( ) =

(f )G x 1 x 2 (f )e j2 f df (9)

where is the time lag, (f ) is the weight dened as a func-tion of frequency, and G x 1 x 2 (f ) is the cross spectral densityfunction

G x 1 x 2 (f ) = X 1 (f )X 2 (f ) (10)where X 1 (f ) and X 2 (f ) are the Fourier transforms of micro-phone signals x 1 (t ) and x 2 (t ), respectively, and denotes thecomplex conjugate. An estimate for the time delay now cor-responds to the lag value maximizing R GCC ( ). An optimalweighting function depends on source signal, the acousticalenvironment, and possible interfering noise. The standardcross-correlation function is obtained with XC (f ) = 1. Twoother typical choices are

SCOT (f ) =1

G x 1 x 1 (f )G x 2 x 2 (f ) (11)

resulting in the so called smoothed coherence transform, and

PHAT (f ) =1

|G x 1 x 2 (f )|(12)

which is called the phase transform.

In discrete time implementations some kind of interpolationis needed in order to get better estimates for the time de-lays. Instead of nding the maximum of the phase transform,Brandstein and Silverman [44] tted a line to the phase re-sponse of the cross-spectrum of two microphone signals andused its slope to estimate the delay. Jacovitti and Scarano[52], on the other hand, propose parabolic interpolation of discrete cross-correlation function around its maximum value.They also suggest replacing the computationally expensivecross-correlation with square difference function (ASDF) oraverage magnitude difference function (AMDF) dened as

R ASDF ( ) =1N

N

k =1[x 1 (kT ) x 2 (kT + )]2 (13)

and

R AMDF ( ) =1N

N

k =1|x 1 (kT ) x 2 (kT + )| (14)

where N is the number of samples and T is the sampling pe-riod. With these signal distance measures the estimate fortime delay corresponds to the lag value minimizing the func-tions.

The second step of TDE localization is the determination of source location based on the estimated delays. The TDE of each pair of microphones corresponds to the other half of ahyperboloid with two sheets. Ideally the location estimatefor a source is found as the intersection of all hyperboloidsdened by all microphone pairs in an array. In practice, how-ever, there is always error in the TDEs and source locationneeds thus to be estimated as the best t to available data.Several different error criteria for this t have been discussedin literature. In general the location estimation involves min-imization of a set of non-linear functions and thus requiresnumerical search methods [44]. However, a closed form so-lution using exactly three TDEs derived from four different



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microphone pairs exists [53]. This does not use any averagingto reduce errors caused by noisy TDEs, but it is computation-ally light and can be readily used with the HUT microphoneprobe. A number of closed form approximations to be used

with a larger number of TDEs have also been described inliterature. For a comparison see [54].

Due to inaccuracy in the determination of TDEs, estimationof distance is not reliable for sound sources far from a mi-crophone array compared to the dimensions of the array. Anestimation method for direction only based on TDEs is dis-cussed in [55]. However, for remote sources the estimation of angle of arrival can be alleviated by approximating the hy-perboloid surfaces by cones having a vertex halfway betweencorresponding pair of microphones. With this kind of approx-imation the angle of arrival related to the line combining themicrophones can be written in the form

= cos 1 c

d

(15)

where c is the speed of sound, is the TDE, and d is the dis-

tance between the microphones. In [56] two such angles cal-culated from orthogonal and concentric pairs of microphoneswere used to dene two lines of potential locations in 3-Dspace, one for each side of the plane formed by the micro-phones. The actual location of a source was then approxi-mated with a linear intersection of the lines dened by two ormore microphone quadruples.

With the HUT microphone probe the angle of arrival of asound source can be unambiguously dened with three exist-ing orthogonal and concentric pairs of microphones locatedon x-, y-, and z-coordinate. For better resolution it is ad-visable to use the outer pairs. The procedure is outlined asfollows. Let x , y , and z be the TDEs of the microphonepairs on x-, y-, and z-axis, respectively. With Eq (15) andsome simple trigonometric manipulations the elevation anglecan be written in the form

= tan 1

z

2x + 2y

(16)

and the azimuth is given by

= tan 1

y x

(17)

where the correct quadrant has to be determined from thesigns of x and y .

Reliable time delay estimation is an essential prerequisite fordetermining the location with the previous methods. Sev-eral modications to the basic estimation scheme have beendeveloped in order to improve performance in noisy, multi-source, or reverberant environments. Zhang and Er [57] in-troduced a hybrid of TDE and coherent signal-subspace [49]methods for source localization. Benesty [58] used eigenvaluedecomposition to derive better TDEs in reverberant environ-ments. Griebel and Brandstein [59] argued that reduction of cross-correlation functions to single TDE parameters causesproblems in reverberant conditions. Instead, they estimateda delay vector directly based on cross-correlations betweendifferent microphone pairs. Finally, Liu et al [60] introducedan interesting method for localization of multiple independentsound sources, incorporating features from models of humanbinaural processing.

Applications of source localizationPassive source localization methods have been typically usedfor automatic beam steering in systems where isolated pickupof selected sources is desired. Application areas include for

example teleconferencing, handsfree telecommunication in acar environment, hearing aids, and speech recognition [44].In video conferencing and surveillance systems, steering of acamera based on acoustical source localization has also beendiscussed.

In many active systems only directional localization needs tobe dened using the previous methods. Locations of objectsproducing low order reections can then be easily determinedbased on angles of arrival and times of propagation from theactive sound source to the receiving array. Sonars are typicalexamples of active systems localizing surrounding objects thisway.

Room response measurements are actually not that differentfrom sonar applications, although their emphasis is not onnding out the geometry of a room but on the effect of the ge-ometry and materials on the soundeld. TDE based methodscan, for instance, be used to give more accuracy to directionalanalysis of measured responses. Passive methods can, on theother hand, be utilized in directional noise measurements andlocalization of noise sources. Passive estimation of room re-sponses and geometry is, however, very difficult since it is noteasy to separate several coherent reected signals from eachother without exact knowledge of the original signal.

CONCLUSIONS AND FUTURE WORKSeveral methods related to application of microphone arrayswere discussed. The measurement section introduced meth-ods for directional measurement, analysis, and visualizationof room responses. In the context of recording applications,several directional microphone arrays and techniques for sur-round sound recording were discussed. Some special direc-tional systems related to acoustic communications applica-tions were also described. Finally, the problem of soundsource localization was addressed and the principles of timedelay estimation based localization were introduced. In eachapplication case special emphasis was given to methods thatcan be used with the HUT 3-D microphone probe.

Future work consists of incorporating source localization tech-niques into measurement applications. Automatic extractionand analysis of low-order reections and propagation pathsin a room from measured directional responses is one suchtask. Effective separation of single reections from responsemeasurements could provide new means for analysis of re-ection properties of the walls of the room. New directionaldescriptors for room and concert hall acoustics are also beingdeveloped.

In passive applications, better distance localization based on

known or estimated properties of a room, instead of proper-ties of the emitted signal, is one of the research goals. Futurework also includes examination of microphone array local-ization properties in relation to the human hearing, thus con-necting microphone array techniques with auditory modellingand binaural processing.

ACKNOWLEDGEMENTSThis study is part of the V ARE technology program, projectTAKU (Control of Closed Space Acoustics), funded by Tekes(National Technology Agency). J. Merimaa is supported by



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the Graduate School in Electronics, Telecommunication andAutomation.

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