19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007

Transcription

1 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 27 CALCULATION OF INTERAURAL CROSS-CORRELATION COEFFICIENT (IACC) OF ANY MUSIC SIGNAL CONVOLVED WITH IMPULSE RESPONSES BY USING THE IACC OF THE SOUND FIELD AND THE AUTOCORRELATION FUNCTION OF THE SOUND SOURCE PACS: Zz Shimokura, Ryota 1 ; Tronchin, Lamberto 2 ; Cocchi, Alessandro 2 1 National Institute of Advanced Industrical Science and Technology; Midorigaoka, Ikeda, Osaka, Jaan; ryota.shimokura@aist.go.j 2 University of Bologna; Viale Risorgimento 2, Bologna, 4136, Italy; tronchin@ciarm.ing,unibo.it, alessandro.cocchi@mail.ing.unibo.it ABSTRACT Binaural imulse resonses (BIRs) are measured to clarify the acoustical characteristics of the sound filed in concert halls and oera houses. Since BIRs indicates the transfer function of sound fields, an anechoic source convolved with the BIRs reresents the signal which listeners hear in that sound field. To find out the acoustical characteristics of the original sound source, it is useful to calculate the autocorrelation function (ACF) because the arameters extracted from the ACF closely related to the subjective reference of listeners [1]. This study investigates the relationshi between sound sources and sound fields by comaring the interaural crosscorrelation function (IACF) of BIRs and IACF of an anechoic source convolved with that BIRs. It can be said that the convolution and correlation are the most imortant calculative techniques in the room acoustics, and the convolution and correlation are identical under a certain condition. In this condition, IACC of an anechoic source convolved with the BIRs can be described by the IACC of BIRs and the effective duration τ e of the ACF of the anechoic source. INTRODUCTION Generally acoustical qualities of concert halls and oera houses are evaluated in base of binaural imulse resonses (BIRs) measured in them, and the anechoic music convolved with BIR realizes the virtual sound as it were layed in the sound field. Interaural Cross Correlation Coefficient (IACC) calculated from BIR is one of arameter to evaluate the saciousness of hall. However the value of IACC is changed by the convolution technique in accordance with the kind of musical motif. For examle, one binaural imulse resonse measured in the concert hall in Tsuyama (Jaan) resents.16 for the value of IACC, while the IACC of the symhony Royal Pavane (Orlando Gibbons) convolved with it is.39, and the IACC of the symhony Symhonietta n14 the forth movement (Malcolm Arnold) convolved with it is.32. INTERAURAL CROSS CORRELATION COEFFICIENT (IACC) The sound from one sound source arrives to left and right ears of a listener in the different sound athways. Interaural cross-correlation function (IACF) reresents the interdeendence between left (right) signal at the origin and the right (left) signal at a delay within 1 ms. IACC is one maximum value in the IACF like IACC = T T T T '( t) l ' 2 l r ( t) dt '( t + τ ) dt T T ' 2 r ( t) dt max τ <1 [ms] (Eq. 1)

2 where 2T is the integral interval, τ is the time delay, and (t) is obtained after assing through the A-weighting filter, which corresonds aroximately to the sensitivity of the ear. ACOUSTICAL EVALUATION OF SOURCE SIGNAL Acoustical arameters of autocorrelation function For the blending of sound field and erformance, Ando (1998) roosed τ 1 and τ e to determine temoral acoustical characteristics of sound sources [1]. The τ 1 and τ e are extracted from a normalized autocorrelation function (ACF) as shown in Φ( τ ) 1 T φ ( τ ) = where Φ( τ ) = Φ() '( t) '( t + τ ) dt (Eqs. 2,3) 2T T where 2T is the integral interval, τ is the time delay, and (t) is an original acoustical signal after assing through the A-weighting filter. τ 1 is a delay time of the first ositive eak, and τ e is an effective duration of ACF, defined by the delay time at which the enveloe of the normalized ACF becomes and then remains smaller than.1. Value of τ 1 indicates itch of the signal, and value of τ e is reetitive feature that corresonds to kinds of musical instrument, temo of the motif and attern of laying like legato or staccato. Figure 1.- Definition of (a) τ 1 and (b) τ e in normalized ACF Practical use of ACF for music During a erformance of music, the acoustical characteristics (e.g. itch and temo) are varied as a function of time. Running ACF is necessary to observe the fluctuation of acoustical characteristic [1]. Running ACF is defined by where Φ ( τ; t, T ) φ ( τ ; t, T ) = (Eqs. 4) [ Φ (; t, T ) Φ (; τ + t, T )] 1/ 2 Φ 1 t = + T ( ; t, T ) '( s) '( s + τ ) ds 2T t T τ (Eqs. 5) After assing through the A-weighting filter, normalized ACF of (t) is calculated in the range of integral interval 2T that is sliding along the duration of motif.τ 1 and τ e extracted from each running ACF indicate varied acoustical characteristic as a function of time. CALCULULATION OF IACC AFTER CONVOLUTION Convolution technique and IACC A musical motif after convolution with BIR of a hall creates a virtual sound as if the music were layed in the hall. For the sake of convenience, IACC of BIR is termed by and the IACC of the virtual music is termed by IACC AC (After Convolution). 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 2

3 For examle, when a white noise (monaural) is convolved with one BIR, the IACC AC agrees with the of the all-assed imulse resonse. And when a ure tone (monaural) is convolved with one BIR, the IACC AC is always 1 indeendently from the frequency of the ure tone and from the value of the. Reresented values Two kinds of rhythmic musical melody, Melody A and Melody B are used in this study (see Figure 2). Melody A is layed by glockensiel, harsichord, iano, and trumet; and Melody B is layed by harsichord, organ, iano, and strings-ensemble. Totally 8 kinds of anechoic musical motif are generated by MIDI. Figure 2.- Scores of (a) melody A and (b) melody B IACC calculated from BIR is unique value, while τ 1 and τ e calculated from the music and IACC calculated from the convolved music with BIR are obtained from the running ACF and running IACF. Since the musical motif continues for 1 s, 1 values either of τ e or IACC AC are obtained when the running ste is.1 s in (Eq. 4). Reresented values for τ e by running ACF and IACC by running IACF and are determined resectively by 5% and 75% robabilities of cumulative frequency when the 1 values either of τ e or of IACC are converted into a histogram. And they are termed τ e (5%) and IACC AC (75%). Relationshi between and IACC AC Figure 3 shows the relationshi between and IACC AC (75%) according to the 8 musical motifs. We used 6 kinds of BIR that were measured in Kirishima International Concert Hall (Jaan), Tsuyama Concert Hall (Jaan) and ancient theatre of Delhi (Greece). IACCAC(75%) (a) (b) (c) (d) IACCAC(75%) (e) (f) (g) (h) Figure 3.- IACC AC (75%) of virtual sound as a function of. (a) Melody A by glockensiel, (b) Melody A by harsichord, (c) Melody A by iano, (d) Melody A by trumet, (e) Melody B by harsichord, (f) Melody B by organ, (g) Melody B by iano and (h) Melody B by stringsensemble. These relationshis have same tendency and can be fitted by ower regression curves, such that α IACC AC = (Eq. 6) Table I shows the exonent α and the correlation coefficient for the fitting R 2. Although IACC AC could be estimated exactly by for the most musical motifs, Melody B by organ is unsuitable for the estimation by Eq. 6. And it has a tendency that the estimated IACC AC of 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 3

4 Melody A is more accurate than that of Melody B. Since Melody B is comosed by a series of chords (see Figure 2 (b)), the IACC AC is changed largely according to the moment sounding or maintaining the chords. Melodies including legato and tenuto laying are difficult to determine the one reresented value of IACC AC, and the estimation of IACC AC by Eq. 6 tends to lead the errors. Table I.- Exonent α in Equation (6) and correlation coefficient for the fitting R 2. Musical motif α R 2 Melody A by glockensiel.38.9 Melody A by harsichord 6.95 Melody A by iano 7.96 Melody A by trumet 1.97 Melody B by harsichord Melody B by organ Melody B by iano.33 Melody B by strings-ensemble Figure 4 shows α in Eq 6 as a function of τ e (5%) of musical motifs. When τ e of musical motif is short, the value of α aroaches to 1. For the signal of white nose, the τ e is theoretically and α becomes 1. On the other hand, when τ e of musical motif is long, the value of α aroaches to. This means that the α value of ure tones (τ e = ) becomes. 1. α τ e (5%) [ms] Figure 4.- Value of α as a function of τ e (5%) of musical motif As a result of asymtotic curve regression, the relationshi between α and τ e (5%) is exressed by 21.7 α = (Eq. 7) (5%) τ e The values of α calculated by Eq. 7 are highly correlated with the measured values (R 2 = 2). The relationshi between IACC AC (75%) and in this theory is illustrated in Figure 5 (a). When the value of α is 1, IACC AC is equal to, which indicates that the convolution with motif similar to noise do not modify the interaural correlation between left and right imulse resonses. When the value of α is, IACC AC is always equal to 1, which indicates that a ure tone motif generated in a hall is not affected by the sound field in terms of IACC and the value of IACC is always 1. Using Eqs. 6 and 7, the estimated value of IACC AC (75%) is calculated by τ e (5%) of the musical motifs and. Figure 5 (b) shows the estimated IACC AC as a function of IACC AC. The τ e (5%) of musical motif convolved with exlain IACC AC (75%) accurately. 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 4

5 1. (a) α = 1. (b) IACC AC (75%) α = α = α = α =1. α = Estimated IACCAC IACC AC Figure 5.- (a) Theoretical relationshi between IACC AC (75%) and according to α. (b) Relationshi between IACC AC and estimated IACC AC by Eqs. 6 and 7. The correlation coefficient (R 2 ) among them is.94. SUBJECTIVE DIFFUSENESS FOR MUSIC CONVOLVED WITH BIR Psycho-acoustical exeriments are conducted for subjective diffuseness erceived from the virtual sound (music convolved with BIR). For realizing virtual sound fields, stereo-diole method is utilized in an anechoic chamber. The aim of exeriments is to verify that the subjective diffuseness is changed, when various musical motifs are erformed in a same sound field. Presentation of sound fields The stereo-diole method is a virtual source imaging system that comrises two closely saced loudseakers (see Figure 6). Using this method and a BIR measured in a hall, same acoustic of the hall can be reresented in an anechoic chamber. In this method, a cross-talk canceling filters are generated based from a BIR measured in the chamber. Generally, sound from the left loudseaker arrives to the left and right ears of a listener. However, using interferences of sounds from two loudseakers, the left side sound assing through the cross-talk canceling filter arrives only to the left ear of the listener. Figure 6 shows the schematic design of the single stereo-diole method using two frontal loudseakers. Adding two rear loudseakers and using 4 loudseakers in the same time, the system is termed dual stereo-diole. Binaural Imulse Resonse BIRr Cross-talk canceling filter frr frl Listener BIRl flr fll Figure 6.- Schematic design of stereo-diole method When the same dummy head used in acoustical measurements of halls is ut on the osition of listener, and a measured BIR of hall is recorded again through the cross-talk canceling filters, a virtual BIR can be obtained. By comaring the measured BIR and the virtual BIR, the accuracy of the stereo-diole method is verified. Figure 7 shows the comarisons of IACC calculated from the measured BIR and the virtual BIR, when the dual stereo-diole method was conducted. In this case, the dual stereo-diole method was systemized in a semi-anechoic chamber (Arlecchino listening room in Bologna), in which reverberation in low frequency (< 5 Hz) remain again. The dual stereo-diole method is excellent for reresenting the satial characteristics of the sound fields. 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 5

6 IACC k 2k 4k 8k 16k k 2k 4k 8k 16k Frequency [Hz] Frequency [Hz] Figure 7.- Comarison of IACC calculated from the measured BIR ( ) and the virtual BIR ( ). The red lines indicate just noticeable differences (JNDs). The BIRs were measured in Kirishima International Concert Hall (left) and in Tsuyama Concert Hall (right). Procedures Two-Alternative-Choice Forces (2ACF) is conducted for the sycho-acoustical exeriment. A subject is resented two stimuli alternatively, and answers which stimulus is erceived more diffusely. By reeating 2ACF, stimuli can be arranged following the subjective order based on the diffuseness. DISCUSSION To evaluate diffuseness in concert halls or oera houses, Farina (21) utilized IACC calculated with all-assed BIR (IACC E ) [2], while Hidaka and Beranek (2) utilized the average of IACCs calculated with.5, 1, and 2 khz band-assed BIR (IACC E3 ) [3,4]. As a result, Farina did not find a correlation between IACC E and subjective evaluation of halls, while Hidaka et al. described that IACC E3 had a high correlation with a rank order of halls acoustical qualities. Although many reasons might exlain this contradiction (e.g. different methodologies of evaluation or different subjects), it is a fundamental roblem that the values of IACC treated by them are calculated by BIR of different frequency ranges. Hidaka and Beranek used the IACC E3 considering about the blending of sound field and erformance, because sectral energy of symhony distributes mainly around.5-2 khz. It is imortant to evaluate the sound quality in halls based on the music erformed in them [1]. The relationshi between, calculated from the measured BIR, and IACC AC, calculated from the musical motifs convolved with BIR was exlained [5]. Theoretically the IACC AC exceeds according to kinds of musical motifs, and the gain can be accessed by the effective duration τ e of ACF of the musical motif. However, ractically, it is no idea that the subjective diffuseness is also increased according to the τ e of ACF. In this study, utilizing the virtual source imaging system stereo-diole method, sycho-acoustical exeriments are conducted to research the subjective diffuseness erceived from the musical motifs convolved with BIRs. The dual stereo-diole method using 4 loudseakers are useful to reroduce the satial characteristics of sound fields in an anechoic chamber (see Figure 7). References: [1] Y. Ando: Architectural Acoustics, Blending Sound Sources, Sound Fields, and Listeners. Sringer, New York (1998) [2] A. Farina: Acoustical quality of theatres: correlations between exerimental measurements and subjective evaluations. Alied Acoustics 62 (21) [3] T. Hidaka, L. L. Beranek: Objective and subjective evaluations of twenty-three oera houses in Euroe, Jaan, and the Americas. Journal of the Acoustical Society of America 17 (2) [4] ISO/DIS 3382, Acoustics: Measurement of the Reverberation Time with Reference to Other Acoustical Parameters. International Organization for Standardization. (1997) [5] R. Shimokura, L. Tronchin, A. Cocchi, V. Tarabusi :Satial imression of music signals after convolution technique. Proc. of Forum Acusticum 25 (25) th INTERNATIONAL CONGRESS ON ACOUSTICS ICA27MADRID 6