Fernandez Comesana, Daniel

Holland, Keith R.

Morales Cervera, Sandra

Takeuchi, Takashi

English

Southampton (e-Prints Soton)

MEASURING MUSICAL INSTRUMENTS DIRECTIVITYPATTERNS WITH SCANNING TECHNIQUESDaniel Fernandez Comesa˜ naMicroﬂown Technologies, Tivolilaan 205, Arnhem, NL. email: fernandez@microﬂown.comTakashi Takeuchi, Sandra Morales Cervera and Keith HollandInstitute of Sound and Vibration Research, Southampton SO17 1BJ, UKCharacterizing directivity patterns of musical instruments implicitly requires measuring non-stationary sound ﬁelds. A priori, this fact implies using multichannel methods to assess anychange along time at all regarded positions. However, this paper explores the advantagesof using a static reference sensor close to the musical instrument to track any variations inthe sound ﬁeld during the measurement, allowing scanning techniques to be performed. Themethod developed is based on taking transfer functions between the scanning transducer andthe reference sensor. Then, the number of positions measured is limited for each frequencydepending on the dynamic range acquired. Experimental results of violin directivity patternsare presented along with a discussion focused on comparing the technique proposed with con-ventional multichannel measurement methods.1. IntroductionHuman understanding is mainly based on seeing; leading people to create many visual repre-sentations to help understanding what is going on when things cannot be seen. Sound representationshave been key aids for understanding practical problems regarding noise issues. Many different tech-niques have been implemented over years for charting sound ﬁelds and noise sources but always witha trade-off between cost, time and accuracy.Already from the late 1980’s scan-based methods have been introduced for mapping stationarysound ﬁelds [1]. Recent works have introduced a novel scanning method called “Scan & Paint” [2–4]for measuring sound pressure, particle velocity, intensity, sound absorption and acoustic impedancein an efﬁcient way. The properties of the sound ﬁeld are determined and visualized via the followingroutine: while the probe is moved slowly over the surface, pressure and velocity are recorded and, atthe same time, a video image is captured. Next, all data is processed. At each time interval, the videoimage is used to determine the location of the sensor. The absolute position of the probe is unknown,only the 2D coordinates relative to the background image are computed. Then, an acoustic color plotis generated.Scanning methods are proven to minimize the measurement time and cost, but conventionallyconstrained to mapping stationary sound ﬁelds. In the literature of Near ﬁeld Acoustic Holography(NAH), several signal processing techniques have been proposed to overcome some problems de-rived from the degree of time stationary of the source [5–7]. However, these techniques require usingmultiple references along with scanning microphone arrays. In contrast, this paper is focused on pre-senting an effective method for directly visualizing sound radiation patterns without back-propagatingICSV19, Vilnius, Lithuania, July 8–12, 2012 119th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012the sound ﬁeld to the source and using only one ﬁxed and one moving sensor.The sound radiation patterns of a musical instrument is a classic example of non-stationarysound source. There are no standard regulations regarding the measurement procedure required forcharacterizing their directivity patterns due to its practical difﬁculties. Directivity patters play animportant role on virtual acoustics, specially when computing room auralizations [8]. Therefore,ﬁnding a measurement technique which allows to characterize the sound radiated of a non-stationarysource in a fast and efﬁcient way will simplify the process remarkably.The following sections will present the theory and methodology required to implement theproposed measurement technique. Furthermore, the directivity patterns of a violin are presented.Finally, advantages and disadvantages of the novel technique are discussed.2. TheoryThe problem addressed by this article is depicted in Figure 1. A scanning pressure microphoneismovedacrossaplanarsurfacewhichhasaseparationdistanceR withthesoundsource. Thissectionderive the theoretical basis required in order to understand how to extract directivity information usingonly two transducers.Figure 1. Sketch of the assessed problemAny complex sound source can be represented as a set of monopoles closely distributed inthe space. The superposition of two or more monopoles under free ﬁeld conditions will generate apressure sound ﬁeld which can be modeled asp(;';r;t) =ArD(;')ej(!t kr) (1)where A is a complex time independent term which relates source characteristics such as volumevelocity, speciﬁc acoustic impedance and wavenumber; ! is the angular frequency; r is the distancebetween source center and measurement plane; and D(;') is a directivity term which can take ar-bitrary values for different radiation angles of azimuth () and elevation ('). Evaluating the aboveexpression for simple sources such as a monopole source, D(;') will simplify to unity for all possi-ble angles. In contrast, D(;') could also be expressed using ﬁrst order Bessel functions if the sourcebehaves as a bafﬂed circular piston [9]. In contrast, musical instruments cannot be described usinggeneral analytical expressions. Consequently, suitable measurement procedures for characterizingcomplex sound sources are required.219th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012Let us now evaluate Equation (1) for the two transducers shown in Figure 1. First of all, theﬁxed reference position can be deﬁned such asp(^ ; ^ '; ^ r;t) = pref(t) = Bej(!t k^ r) (2)where B is a complex time independent term which relates source characteristics perceived at a givenposition ^ ; ^ '; ^ r. It is important to highlight that the number of independent variables have been re-duced but the time dependency is maintained. Secondly, it is necessary to deﬁne the projection ofeach of the measured pressures across the measurement plane in a sphere of radius R, i.e.psph(;';t) = p(;';r;t)R + rRejr (3)where r represent the euclidean distance between the corresponding sphere projection and the mea-surement position. Figure 2 shows an example of the sound ﬁeld produced by a monopole sourcemeasured in 6 equidistant planar planes and the corresponding directivity pattern obtained after pro-jecting the data into a sphere.Figure 2. Example of a monopole radiattion measurements transformed to a spherical directivity patternSofar, arbitrarysignalsinthetimedomainhavebeenassessed. However, bydeﬁningatimehar-monic excitation we can relate Equation (2) and Equation (3) in the frequency domain by computingthe transfer function estimator H1 such asH1(;';!) =Ffpsph(;';t)gFfpref(t)g= D(;')A(!)B(!)e jkRR(4)where Ffg denotes time Fourier transform. Since the right hand side of Equation (4) is independentof the position of the moving sensor we can demonstrate that the transfer function estimator H1 couldbe understood as a scaled version of the directivity term D(;'), henceH1(;';!) = D(;')(!) (5)where (!) is a scaling factor which depends on the position of the reference sensor, radius R and thesource characteristics. From Equation (5) can be inferred that measuring transfer function betweenﬁxed and projected signals leads to a time independent expression for calculating the directivity ofany sound source. This key factor allows using scanning techniques even though the source excitationis non stationary. Tracking the position of the moving sensor across time make possible to represent319th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012transfer function variations across space, which are directly related with the radiation patterns of thesound source. Nevertheless, errors could appear if not only the absolute level varies but also thespectral content changes along time. An algorithm for selecting the spatial positions depending onthe dynamic range of the assessed frequency is presented in the next section in order to overcome thispotential problems.In summary, it has been shown analytically that the transfer functions between a ﬁxed and amoving transducer gives a time independent ratio which carries information about the directivity ofthe sound source assessed.3. Positional discrimination algorithmSo far it has been pointed out that taking transfer functions between a ﬁxed and a moving trans-ducer allows to characterize time independent relative variations across a sound ﬁeld. Nonetheless,a detailed description of the measurement scenario is required to understand how to apply a posi-tional discrimination algorithm. Figure 3 shows a schematic view of a generic experimental setup.This ﬁgure illustrates how a continuous time signal is driving the sound source while the scanningmicrophone is moving across the sound ﬁeld. A ﬁnite grid of positions can be created relative tothe location of the moving transducer. Then, the time intervals (t1;t2;:::;tn) can be linked with theircorresponding measurement positions (x1;x2;:::;xn).Figure 3. Schematic view of the measurement scenarioNext, the time sequences measured with the moving and static sensors are combined by com-puting the transfer function estimator H1 (see Equation (4)). This allows to assess how the soundradiation changes across the space. Nonetheless, it is required to have sufﬁcient spectral excitation atthe source so as to evaluate this power spatial changes. Hence, the Power-Spectral Density (PSD) ofthe ﬁxed transducer can be studied for different time intervals so as to neglect transfer functions withpoor signal to noise ratio.A maximum dynamic range has been establish depending on the maximum transfer functionfound for each frequency band. Consequently, any position with insufﬁcient signal excitation for agiven frequency has been disregarded. This leads to have an irregular spatial grid which size changesacross the frequency domain. Figure 4 shows a representation of the procedure.In summary, transfer functions have been mapped across space depending on the excitationsignal. The spectrogram of the reference sensor is assessed for each position to see whether there isenough excitation on the source for each particular frequency.419th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012Figure 4. Diagram of the positional discrimination procedure4. Instrumentation and experimental setupScanning measurements were carried out using a Microﬂown PU probe which contains a pres-sure microphone along with a particle velocity sensor. The reference pressure microphone used wasa Read Instrument Microphone Fiddle Pro. This hyper-cardioid microphone was attached to the Cbout of the violin by a stainless steel spring clip. In addition, a camera “Panasonic Lumix TZ7” wasrequired for recording a video of the measurements.Measurements were performed in the large anechoic chamber of the ISVR (Southampton, UK)for achieving free-ﬁeld conditions. The sound radiation of a violin was measured carrying out sweepsone meter away from the musical instrument along surfaces of two meters by two meters.Six different planes were scanned without modifying the measurement setup: the musician wasturned around the radiation center for the front, left, right and back plane and then she had to performlying on a table so as to capture the top and bottom radiation. The excitation signal measured was atraditional music piece. The time expended in each scanning was about 4 minutes.In addition, Figure 5 presents a picture of the measurement setup in the ISVR anechoic chamber(left) along with a spectrogram sample extracted from one the measurements performed. As can beinferred from this ﬁgure, the statistical properties of short time segments of the excitation signal arenot representative of the whole time series. Consequently, it can be conclude that the measurementswere performed under non time stationary conditions.Figure 5. Experimental measurement setup (left) and spectrogram sample (right)519th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 20125. Presenting resultsOne common visualization methods for presenting 3D directivity patterns is using colormapsoverlay on a mesh of the geometry used. It gives a direct feedback about radiation maxima but itis not enough clear to follow the pattern variations across the space. Consequently, it is commonpractice using polar coordinates scaling the radius of the point aimed to represent according to thevalue represented by the color. Figure 6 illustrates the two representation methods explained. Thedata used in both cases corresponds to the scaled directivity described in Section 2.Figure 6. Example of a monopole radiattion measurements transformed to spherical directivity pattern6. Directivity patternsFigure 7 presents several examples of the measured directivity patterns at four different thirdoctave frequency bands: 315 Hz, 500 Hz, 1000 Hz and 1588 Hz. The X plane represent the frontalmeasurement plane. Hence, only the frontal, top and right directivity can be seen in the given ﬁgure.According to the measurement results the violin has an omnidirectional behavior at the lower fre-quency bands. In contrast, as frequency increases the directivity patterns shapes change dramatically,moving the radiation lobe from the front of the musician to the side, depending on the frequency bandassessed.7. Advantages and disadvantages of the measurement procedureCurrent methods for measuring non-time stationary sound ﬁeld rely on using large sensor ar-rays. The most common solution uses one sensor for each measurement position. Alternatively,methods based on NAH can reconstruct the entire sound ﬁeld by placing multiple reference trans-ducers and then scanning an area with a large array [5]. The novel technique proposed in this paperonly requires two sensors: one static while the other is manually moved. Time, cost, simplicity, ﬂexi-bility and accuracy are the main issues evaluated in this section which determine the advantages anddisadvantages of choosing a measurement technique.Time required for setting up the instrumentation and performing the measurement is always abig issue. Manual sweeps of a single probe are a fast procedure for directly obtaining informationabout a sound ﬁeld. Each measurement plane was evaluated undertaken sweeps for less than 4 min-utes, which can be seen as a reasonable amount of time for characterizing the sound ﬁeld producedby a non-stationary sound source such as violin.619th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012Figure 7. Directivity patterns of a violin at third octave bands of 500 Hz (top left), 1000 Hz (top right), 1260Hz (bottom left) and 1588 Hz (bottom right) [dB]One of the main problems of most conventional array measurement systems is the cost of theequipment. Not only the number of transducer required for performing the measurements but also themultichannel acquisition system rise the price strongly. The proposed two-sensor solution has far lessrequirements than most of the current large multichannel applications.The measurement protocol and the post processing stage should be fairly intuitive. The useof a camera makes sure that all the measurement process is ﬁlmed . This has been proved to behelpful with trouble shooting. Color maps overlaid on pictures give a direct feedback that is easy tounderstand.The ﬂexibility of the proposed method is one of its stronger advantages against array-basedsolutions. The novel technique allows to setup all instrumentation and resize the measurement planejust by moving the camera. Furthermore, the spatial resolution of the measurement is selected afterperforming the measurement allowing to assess several spatial distribution a posteriori. The criteriafor selecting the blocks size of the grid depends on the frequency investigated and the duration of themeasurement (as the sweep get longer the grid blocks can be smaller).The main outcome of a measurement technique is to ensure accurate and reliable results. Thesmooth radiation maps presented in Figure 7 support the great potential of combining the Scan &Paint measurement techniques with the positional discrimination algorithm. The more measurements719th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012per plane, the more accurate the results will be since the small errors due to human factors can beminimized when averaging all the sessions. Besides, the fact that there are not physical ﬁxed positionsleads to minimize the interference effect of placing so many objects in the sound ﬁeld.8. ConclusionsA theoretical base for measuring time independent relative changes in a sound ﬁeld has beenderived. Moreover, an algorithm for selecting the spatial areas with same signal excitation has beenproposed. The combination of the described principles with the scanning measurement techniqueScan & Paint lead to a novel method for characterizing directivity patterns of non-stationary soundsources using a scan based two-channel system. Results presented support the successful imple-mentation of the method. The measurement technique presented reduces the number of transducers,measurement time and cost, while maximizes the ﬂexibility of current methods.References1 J.Hald. Stsf-auniquetechniqueforscan-basednear-ﬁeldacousticsholographywithoutrestrictionson coherence. Technical report, Bruel & Kjaer, 1989.2 E. Tijs, H.-E. de Bree, and S. Steltenpool. A novel acoustic pressure-velocity based method toaccess acoustic leakages of an acoustic enclosure in non anechoic conditions. In Euronoise, 2009.3 E. Tijs, H.-E. de Bree, and S. Steltenpool. Scan & paint: a novel sound visualization technique. InInternoise, 2010.4 H.-E. de Bree, J. Wind E. Tijs, and A. Grosso. Scan & paint, a new fast tool for sound sourcelocalization and quantiﬁcation of machinery in reverberant conditions. In VDI Maschinenakustik,2010.5 J. Hald. Non-stationary stsf. Technical report, Bruel & Kjaer, 2000.6 Moohyung Lee and J. Stuart Bolton. Scan-based near ﬁeld acoustical holography and partial ﬁelddecomposition in the presence of noise and source level variation. Journal of the Acoustical Societyof America, 119:382–393, 2005.7 H.-S. Kwon, Y.-J. Kim, and J. Stuart Bolton. Compensation for source nonstationarity in multiref-erence, scan-based near-ﬁeld acoustical holography. Journal of the Acoustical Society of America,113:360–368, 2003.8 Sandra Morales-Cervera. Virtual reality system for musical performance practice. Master’s thesis,Institute of Sound and Vibration Research, 2011.9 L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders. Fundamentals of Acoustics. SponPress, 3rd edition, 1982.8

A novel acoustic pressure-velocity based method to access acoustic leakages of an acoustic enclosure in non anechoic conditions.

Compensation for source nonstationarity in multireference, scan-based near-ﬁeld acoustical holography.

Fundamentals of Acoustics.

Non-stationary stsf.

on coherence.

Scan & paint, a new fast tool for sound source localization and quantiﬁcation of machinery in reverberant conditions.

Scan & paint: a novel sound visualization technique. In Internoise,

Scan-based near ﬁeld acoustical holography and partial ﬁeld decomposition in the presence of noise and source level variation.

Virtual reality system for musical performance practice.

Measuring musical instruments directivity patterns with scanning techniques

Measuring musical instruments directivity patterns with scanning techniques

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