Applition of high-speed line sn mer for ousti mesurements of virting ojets Mirko Mustonen, Dmitri Krtofelev, Antoli Stulov Lortory of Nonliner Dynmis, Institute of Cyernetis t Tllinn University of Tehnology, Tllinn, Estoni. Ves Välimäki Shool of Eletril Engineering Deprtment of Signl Proessing nd Aoustis, Alto University, Espoo, Finlnd Summry A novel high ury experimentl equipment for the detetion nd mesurements of virting ojets hs een designed nd uilt. The set-up onsists of high frme rte line sn mer nd ustom-uilt optil lens system. The optil tue is designed to provide suient mgnition, in order to reord the motion of smll prts of musil instruments suh s thin strings. Also, the mgnition helps to register smll virtion mplitudes. The experimentl set-up gives possiility to perform urte high qulity onttless mesurements of virtion of vrious prts of musil instruments, suh s the strings, neks, soundords, ridges, et. The high temporl resolution of the mers llows to pture the eets ssoited with vrious spets of dispersion in the strings. The set-up hs een lirted nd suessfully used to mesure pino nd ss guitr string virtions. In ddition, roust method for the virtion dt extrtion from the reorded video is presented. PACS no. 43.25.Zx, 43.4.Cw, 43.75.Tv, 43.4.At. Introdution In the eld of musil oustis, the virtion mesurements of vrious prts of stringed instruments re importnt to determine nd desrie the underlying physis. Of gret interest is the virtionl motion of strings, neks, frets, ridges nd soundords. The onttless string virtion mesurement methods n e divided into three tegories: the eletromgneti, the eletri eld sensing, nd the optil. The eletromgneti methods exploit the Frdy's lw. The priniple of the string displement detetion is the following: the eletromgneti oil is pled ner the string, nd the motion of the string indues voltge in the iruit tht is proportionl to the string's veloity. By integrting the veloity signl, the displement of the string n e otined. This method ws used nd desried in []. Eletromgneti devies, similr to the nonliner pikup of the eletri guitr re the most ommon wy to detet the string virtions [2]. The eletri eld sensing mkes use of the phenomenon, where the pitne etween two eletrodes hnges, when the distne etween them is () Europen Aoustis Assoition vried. In the simplest pproh, onduting string is grounded, nd DC voltge is pplied to n eletrode plte nery. The string's movement modultes the voltge etween the string nd the plte, nd informtion out the string's plement is otined f. [3]. The prinipl drwks of the eletromgneti nd eletri eld sensing re the fts tht these methods work only for onduting (metl) strings, nd they slightly inuene the string's motion y dmping it. In ddition, these devies require extensive lirtion, efore one n strt otining meningful dt. The limits nd enets of these methods re disussed in [, 3]. The optil methods of virtion mesurement tht n detet virtion of neks, frets, ridges or soundords in ddition to string virtion, exploit vrious light or lser emitting nd deteting sensors. For exmple, the high speed digitl mers with pproprite video dt proessing proedures n e suessfully used to mesure string virtion [4]. Also, the dierent devies tht onvert lser light into uniform prllel em nd detet (with CCD, CMOS sensors) the loked light (shdows) n ensure the result [5], f. [6]. This tehnology my e rther expensive when high qulity dt with high sptil or temporl resolution is desired. Dierent lser virom-
FORUM ACUSTICUM 24 7-2 Septemer, Krkow Mustonen et l, R: Applition of high-speed line sn mer z y Cmer String Light soure Figure. Two mer set-up. Arrows indite the diretion of light propgtion. eters n suessfully detet the surfe virtion of soundords with high ury. The devies tht re sed on vrious photovolti detetors hve lso een reltively suessful [7, 8, 9]. The min lk in using these ustom uilt devies is tht they require extensive lirtion. In this pper we desrie nd nlyse novel optil virtion detetion tehnique, whih is esy to set up s well s to use, nd whih produes highqulity high-resolution mesurement dt. This experimentl mesurement method ws lso onsidered in [,, 2]. The method presented is reltively inexpensive, does not require preliminry extensive lirtion, nd it n detet the motion of ojets mde of ny mteril. The virtion motion is mesured y mking use of the ommerilly ville high-speed digitl line sn mer. 2. Mesurement equipment A line sn mer diers from usul digitl video mer y the imge sensor geometry. Usully the video mer sensor's pixels re pled in rows nd olumns tht form grid. The line mer sensor onsists only of single (or ouple) pixel rry(s). This mkes them less expensive, ompred to usul high-speed mers. We propose to use ommerilly produed high-speed line sn mers tht hve the glol shutter tehnology. This mens tht ll pixels pture light simultneously, nd therefore no imge distorting lgs inuene the result. In this reserh we use two monohrome Teledyne Dls Pirnh2 (k 67 khz) line sn mers. These mers hve 24 x pixel CCD sensors nd frme rte up to 67 frmes per seond (fps). Pixel depth output is seletle etween 8 or its. The physil dimensions of the mer re 5 x 85 x 5 mm, mking them quite smll ompred to the usul high-speed video mers. These ompt mers n e pled in nrrow vities, whih my e eneil when mesuring rel musil instruments. In ddition, mers require Xeler-CL PX4 Dul frme-grer iruit ord tht n e onneted to usul PC's motherord vi PCI Express x4 slot. The frme-grer Cmer 2 z y Mirror String Light soure Figure 2. Single mer nd mirror set-up. Arrows indite the diretion of light propgtion. onnets the PC with the mers, nd is used to ontrol them, nd to reeive the reorded dt. The mers n e mounted with suitle ommerilly ville tele-mro or mro lenses. We use ustom uilt optil tue, ssemled from spre prts purhsed from the Thorls produt tlogue. The tue with n djustle length is tted with plno-onvex lens tht hs suitle fol length. The orret ojet distne, fol length (tue length), nd mgnition vlues re otined y using the theory of thin lenses. Two possile set-up ongurtions nd methods of mesuring re presented in the next susetions. 2.. Two mer set-up By pling two mers under the right ngle (9 ), one n reord the virtion of desired point on the string in oth virtion polriztions simultneously. Figure shows the shemti drwing for the two mer set-up. The mer is reording the position of the string with respet to the horizontl xyplne, nd the mer 2 reords the motion with respet to the vertil xz-plne. Here it is ssumed tht the diretion of the string t rest denes the x-xis. Cmer 2.2. Single mer nd mirror set-up If sitution lls for it, single mer my e used in omintion with mirror. The mirror should e pled ehind the string under 45 ngle with respet to the optil xis of the optil tue, s shown in Fig. 2. Hlf of the reorded imge will ontin displement dt for the vertil, nd the other hlf for the horizontl diretion. This set-up hs some deienies ompred to the previous set-up ongurtion. It is diult to fous the imge entirely, euse the mirror imge of the string ppers further ompred to the string itself. Some ompromise in the imge qulity hs to e mde y using the thin lenses with short fous length. In ddition, the eetive sptil resolution (pixels per spe unit) of the otined imges is two times lower. In oth experimentl set-up ongurtions, one should provide plentiful mount of light. Espeilly, in se if one reords the virtion using high fps vlues, nd the exposure time eomes extremely short.
FORUM ACUSTICUM 24 7-2 Septemer, Krkow Mustonen et l, R: Applition of high-speed line sn mer Pixel no. (x)..8 5.6.4.2 5...2.4 2.6 3.8 4. 5 Frme no. (x) Figure 3. Imge les s reorded y the line sn mer under dierent lighting onditions. ) The ss guitr string motion s reorded y using the mer nd mirror set-up. Top hlf of the imge shows the displement u z nd ottom hlf the u y. ) The pino string's vertil displement u z s reorded y single mer. Thus, requiring powerful light soure in order for the ojet to e registered y the light sensitive sensor of the line mer (vide Figs., 2). 2.3. Clirtion nd optil errtion Figure 3 shows exmples of reoded video dt. Sine the imge sensor of the line mer onsists of single pixel rry, the reorded video n e represented s 2D imge, where the vertil xis signies the pixel numer, nd the horizontl xis orresponds to the reorded frme numer. The imges in Fig. 3 re tken under dierent lighting onditions, nd for two dierent strings. The detiled informtion of the used strings, nd the exittion mnner is provided in Se. 4. The lirtion of the frme pixel numer to the spe sle, nd the frme numer to the time sle is hieved s follows. The known frme rte of the reorded video (imge) is used to mp the time sle with the frme numers. To estlish the lirtion reltion etween the pixel numers nd the spe units, n ojet with known dimensions is used. We use pper with thin prllel lines drwn on it. It ws empirilly determined tht the imge errtion of proposed optil tue ws insignint. This onlusion holds for the following rnge of the set-up prmeters: the string deetion mplitudes < 5 mm; the ojet distne 3 8 mm; the lenses with fol lengths 25 5 mm; the desired imge mgnition up to three times. 3. Virtion dt extrtion Depending on the qulity of the otined imges (videos), two methods of imge nlysis for the extrtion of string displement dt n e pplied. For imges tht hve poor qulity (i.e., out of fous, the vrition in pixel depth is smll, speulr reetion, et.) the imge frme orreltion method is reommended. In se of high imge qulity (i.e., good Pixel depth level 8 6 4 2 p k 2 4 6 8 Pixel no. (x) Figure 4. The orreltion of single frme. Solid line p shows the reorded imge prole. The orreltion kernel k is shown y dotted line. The orrelted frme prole is shown y dshed line. Vertil line show the position of the imge region tht is most similr to seleted kernel prole. Higher depth levels orrespond to imge regions with higher illumintion. ontrst nd no reetion) the edge detetion lgorithms n e used [3, 4]. 3.. Frme orreltion method The frme orreltion method is sed on the disrete D orreltion integrl trnsform. Figure 4 shows n exmple of the pplition of the method. The light reeted from the string retes digitl imprint of mesured ojet's shpe p. In order to extrt the plement informtion of the digitl impression of the string p of the reorded frme, kernel k is onstruted. The kernel is seleted to e similr in shpe to the imge p feture we re interested in trking. By orrelting p with k, orreltion frme prole is otined. As one n see resulting prole hs shrp mximum (shown y ullet). This mximum orresponds to the position of the seleted imge feture, nd n e understood s the string's deetion position u (shown y the vertil line). The proedure is repeted for ll the remining reorded frmes, thus reonstituting the string's deetion time series. Figure 5 shows how urtely the frme orreltion method is tring the imge of the string (the seleted imge feture). Figure 5 shows the orresponding lirted string displement wveform u(t). 3.2. Edge detetion method As pointed out ove, if the imge qulity is good enough (vide Fig. 3 ), then the existing nd well developed edge detetion pkges n e used. By seleting one of the two edges of the reorded string imge, nd y trking it through ll frmes, the string displement dt re extrted.
FORUM ACUSTICUM 24 7-2 Septemer, Krkow Mustonen et l, R: Applition of high-speed line sn mer Pixel no. u [mm] 6 4 2..5..5 2. Frme no. (x) 2.5 3. 3. 2.. 2 3 4 5 6 7 Figure 5. Virtion of ss guitr G string, with tringulr initil ondition. ) The reorded imge. Displement of the mximum of the orrelted frme reltive to the imge is shown y solid line mrked y ullets. ) The orresponding extrted nd lirted displement u(t).. 9.5 9..5.6..6 2 4 6 8 2.5. 9.5 9..6..6 Figure 6. Virtion of the ss guitr string pluked with n index nger. ) String displement in the vertil diretion. ) String displement in the horizontl diretion. ) String motion with respet to yz-plne. 4. Mesurement exmples In this setion eletri guitr string nd sti pino string virtions ptured y the single mer nd mirror set-up re presented nd desried. 4.. Guitr string virtion The virtion of the G string of solid odied eletri ss guitr Hohner Model B5/Mr is onsidered. The mesured string hs speking length L = 865 mm nd dimeter d =.65 mm. It is tuned to produe tone G 2 (fundmentl frequeny f = 98. Hz). Figure 6 shows the virtion of the string when pluked with n index nger t the point x = 9 mm, mesuring from the guitr ridge. The resulting displement in the vertil diretion u z (l, t), nd in the.4. 9.6..4.8 2 4 6 8 2.4. 9.6.8.4. Figure 7. Virtion of the ss guitr string pluked with pletrum. ) String displement in the vertil diretion. ) String displement in the horizontl diretion. ) String motion with respet to yz-plne. horizontl diretion u y (l, t) mesured t l = 35 mm re shown in Figs. 6 nd 6 respetively. The string's motion with respet to yz-plne is shown in Fig. 6, where typil elliptil trjetory of motion is seen. This result is omprle to the results otined y Pkrinen nd Krjlinen in [3]. Figure 7 shows the virtion of the ss guitr string when it is pluked with plsti pletrum t the point x = 9 mm. In similr mnner, s shown in previous gure, the mesured virtions in the vertil diretion u z (l, t), nd horizontl diretion u y (l, t) re shown in Figs. 7, nd 7 respetively. Figure 7 shows the string motion with respet to yz-plne. The omprison of oth ses revels tht the string pluked with nger hs muh smoother wveform, nd stronger dispersive ehviour oth in the vertil nd the horizontl virtion diretions. Also, the elliptil trjetory of motion in yz-plne of the nger pluked string ppers more ovl ompred to the motion of the string, whih is pluked with pletrum. Shrper wveform proles in the se of the pletrum exittion re responsile for the inresing of the upper prtil ontent of the string motion spetrum. This in turn, is responsile for the guitr timre tht lso hs n enrihed high-frequeny prtil ontent. Figures 8 nd 9 show the string virtion resulting from n initil ondition tht hs tringulr shpe with pek loted t x = 9 mm. The string exittion is performed in the following mnner. A thin otton thred is looped round the string t x = 9 mm nd the string is displed to suitle mplitude in the vertil diretion. A suiently fst snp of the thred is hieved y urning it with me. Figure 8 shows the resulting virtion right fter the
FORUM ACUSTICUM 24 7-2 Septemer, Krkow Mustonen et l, R: Applition of high-speed line sn mer 2 2 3 4 5 6 7 8 2.8..8 Figure 8. String virtion right fter the string ws exited in the vertil diretion. ) String displement in the vertil diretion. ) String displement in the horizontl diretion. ) String motion with respet to yz-plne. Dshed lines indite the mplitude extent in the horizontl diretion. 9 5 5 52 53 54 55 56 57 58 9.8..8 Figure 9. String virtion.5 s fter exittion in the vertil diretion. ) String displement in the vertil diretion. ) String displement in the horizontl diretion. ) String motion with respet to yz-plne. Dshed lines indite the mplitude extent in the horizontl diretion. string is relesed nd Fig. 9 shows the wveform of the sme virtion.5 s lter. Bsed on numerous experiments, it ws estimted tht the proposed method of the string exittion provides the string virtions minly in one virtion plne (xz-plne) for pproximtely 5 periods. The omprison of Figs. 8 nd 9 shows tht with the pssge of time, the string's trjetory of motion in yz-plne hnges nd eomes more omplited. 3 2 2 3 4 5 6 7 Figure. Virtion of sti steel string in the vertil diretion showing the dispersion eet. In ddition, the mplitude of the virtion with respet to the y-xis eomes pproximtely two times lrger. This phenomenom indites tht prt of the trnsversl virtion energy distriuted initilly in vertil plne is trnsferred to the horizontl plne. Most likely this is due to the dierent termintion onditions for the vertil nd horizontl string motion t the guitr ridge nd the guitr nut. 4.2. Sti pino string virtion Figure shows the virtion of sti steel pino string in monohord. The virtion orresponds to the video imge shown in Fig. 3. A monohord is onstruted using steel string of length L = m tht is used in pino mnufturing. The liner mss density of the string µ = 7.8 g/m nd the string's dimeter d =.25 mm. The monohord is tuned to the frequeny of 35 Hz pproximtely. An initil ondition tht hs tringulr shpe with pek loted t the point x = 795 mm is indued y using the otton thred tehnique explined in the previous susetion. The mesuring shows tht the resulting virtion of the string is strongly dispersive. The dispersion is used y the ft tht the high frequeny osilltions trvel long the string fster ompred to the low frequeny wve omponents. The otined results re omprle to previously reported mesurements y Podlesk nd Lee in [5]. 5. Disussion In this pper the virtion exmples of two dierent strings re presented. In the ontext of musil oustis, other virting prts of the stringed instruments like ridges, frets, nd neks hve een suessfully mesured y the uthors. For exmple the virtion of the guitr nek n e mesured y video reording the edge of the nek with the line sn mer, nd pplying the video dt proessing methods desried ove on the reorded video. The mer hs
FORUM ACUSTICUM 24 7-2 Septemer, Krkow Mustonen et l, R: Applition of high-speed line sn mer lso een used to pture fst rottory motion of smll ylindril ojet (dimeter mm), y trking the position of mrking line drwn on the lterl side of the ylinder. For the presented exmples, the optil experimentl set-up of virtion mesurement worked well. However, if sitution demnds it, the method n e improved. Line sn mers with etter sptil resolution, i.e. lrger numer of pixels in the imge sensor, or higher frme rte re ommerilly ville. If reordings of ojet's displement t severl lotions re needed, the multiple sets of mers my e used. The hrdwre solution tht supports the use of more thn two mers simultneously is ville. 6. CONCLUSIONS The novel onttless optil method of virtion mesurement ws demonstrted y mesuring virtions of the eletri ss guitr, nd sti pino string. The reorded videos with the extrted displement dt were presented. The proposed method uses ommerilly ville digitl line sn mer, nd ustom uilt optil tue. Two possile experimentl mesurement set-up ongurtions were presented. It ws shown tht the method does not hve the usul deienies tht re ssoited with the other widely used onttless virtion or string displement mesurement tehniques, suh s methods sed on the eletromgneti or eletri eld sensing, nd methods tht re sed on the vrious photovolti detetors or the high-speed digitl mer usge. A rief overview on the wys to improve the proposed mesurement set-up ws presented. To otin the mesurement results with higher qulity one n purhse line sn mers tht hve higher numer of pixels in the imge sensor or higher reording frequeny (fps vlues). In onlusion, the high-speed line sn mers hve een suessfully used for high qulity, onttless optil virtion mesurements. The reorded virtion dt hd high sptil nd temporl resolution. Aknowledgement The uthors re grteful to Montserrt Pàmies Vilà nd Atkn Kuily for their helpful omments. The work of M. Mustonen, D. Krtofelev nd A. Stulov ws supported y the EU through the Europen Regionl Development Fund, nd y the Estonin Ministry of Edution nd Reserh (SF477s8). The uthors re grteful to the Alto University funding sheme for infrstruture. Conferene trvel expenses of the rst uthor where nned y Dotorl Studies nd Interntionlistion Progrmme DoR T8 (Arhimedes Foundtion, Estoni). PCI Express is registered trdemrk of PCI-SIG (Peripherl Component Interonnet Speil Interest Group). Thorls is registered trdemrk of Thorls, In. Referenes [] A. Askenfelt nd E. V. Jnsson: From touh to string virtion. III: String motion nd spetr. J. Aoust. So. Am. 93(4) (993) 28-296 [2] R. C. D. Piv, J. Pkrinen, nd V. Välimäki: Aoustis nd modeling of pikups. Journl of the Audio Engineering Soiety 6() (22) 768-782 [3] J. Pkrinen nd M. Krjlinen: An pprtus for mesuring string virtion using eletri eld sensing. In Proeedings of the Stokholm Musi Aoustis Conferene (SMAC3), Stokholm, Sweden (23) 739-742 [4] N. Plth: High-speed mer displement mesurement (HCDM) tehnique of string virtion. In Proeedings of the Stokholm Musi Aoustis Conferene (SMAC 23), Stokholm, Sweden (23) 88-92 [5] Y. Ahkire nd A. Preumont: Optil mesurement of le nd string virtion. Shok nd Virtion 5(3) (998) 779 [6] Y.-S. Li, T. Y. Young, nd J. A. Mgerl: Supixel edge detetion nd estimtion with miroproessorontrolled line sn mer. IEEE Trnstions on Industril Eletronis 35() (988) 5-2 [7] R. J. Hnson, J. M. Anderson, nd H. K. Momer: Mesurements of nonliner eets in driven virting wire. J. Aoust. So. Am. 96(3) (994) 549-556 [8] M. Podlesk nd A. R. Lee: A photovolti detetor for string virtion mesurement. J. Aoust. So. Am. 79(6) (986) 292-293 [9] N. Leroy, E. Fléty, nd F. Bevilqu: Reetive optil pikup for violin. In Proeedings of the 26 Interntionl Conferene on New Interfes for Musil Expression (NIME6), Pris, Frne (26) 24-27 [] D. Krtofelev, M. Mustonen, A. Stulov, nd V. Välimäki: Applition of high-speed line sn mer for string virtion mesurements. In Proeedings of Interntionl Symposium on Musil Aoustis (ISMA 24), Le Mns, Frne (24) [6] in press [] M. Mustonen, D. Krtofelev, A. Stulov, nd V. Välimäki, Experimentl verition of pikup nonlinerity. In Proeedings Interntionl Symposium on Musil Aoustis (ISMA 24), Le Mns, Frne (24) [6] in press [2] M. Pàmies-Vilà, I. A. Kuily, D. Krtofelev, M. Mustonen, A. Stulov, nd V. Välimäki: High-speed linemer mesurements of virting string. In Proeeding of Blti-Nordi Aousti Meeting (BNAM), Tllinn, Estoni (24) [8] [3] J. F. Cnny: A omputtionl pproh to edge detetion. IEEE Trns. Pttern Anlysis nd Mhine Intelligene (986) 679-698 [4] J. F. Cnny: A vritionl pproh to edge detetion. In Proeedings of Ntionl Conferene on Artiil Intelligene (AAAI-83), Wshington, D.C, United Sttes of Ameri (983) 54-58 [5] M. Podlesk nd A. R. Lee: Dispersion of wves in pino strings. J. Aoust. So. Am. 83() (988) 35-37