1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 15 0 5 10 15 20 25 30 35 40 AbsoluteMean Relative Error and Standard Deviation RelativeError of Direct Sound AverageInstantaneous Intensity by each Position using thep p probe Position Number [ ] R e l a t i v e E r r o r o f A n g l e o f a r r i v a l [ % ] 45º 15º -45º -75º Direct Sound First Reflection 1st 14th 1st 14th 0º -90º 180º 90º Horizontal Plane oriented on thex-zplane 1 2 3 4 5 6 7 8 9 10 11 1 2 13 14 15 0 5 10 15 20 25 30 35 40 AbsoluteMean RelativeError and Standard Deviation RelativeError of First Reflection AverageInstantaneous Intensity by each Position using thepp probe Position Number [ ] R e l a t i v e E r r o r o f A n g l e o f a r r i v a l [ % ] 6.- References: [1]Heyser, R., Instantaneous intensity, inAES 81st Convention Nov 12-16 1986, Los An geles, CA, U. S.A.1986. [2] Merimaa, J., et al., Measurement, Analysis, and Visualization of Directional Room Responses , i nAES 111th Convention, New York, N.Y., U.S.A., 2001 September 21–24, 2001. [3] Müller, S. and P. Massarani, 'Transfer-Function Measurement with Sweeps' .Journal of the Audio EngineeringSociety, 2001. 49(6): p. 443-471. Fourth Laser pointer on a railway trolleyperpendicular to the metal ruler Third Laser pointer used to measured the acoustic centre of the speaker Fourth Laser pointer used aligned with the rope of the plumb bob Laser pointer combined with plumb bob accuracy± 1 mm Detail of plumb bob at origin of the speaker and mic stand vibration decoupler 1 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 DiffusenessEstimate( )at theplaneXZ in ERB bands Time [ ms] F r e q u e n c y [ k H z ] 100%Specular 90% 80% 70% 60% 50%Specular 40% 30% 20% D i r e c t s o u n d F i r s t R e fl e c t i o n The use of Sound Intensity for Characterisation of Reflected Energy in Small Rooms 1.- Objectives: a) T o develop a measurement system aiming t o measure the strength, tempor al and spatial properties of Early sound field in Small Rooms with a spherical resolution similar to the Minimum Audible Angle ( MAA = ± 2º at the front). b) To find out useful descriptors to characterise the acoustic of the Early Reflection energy in small rooms. Julián Romero-Pérez, Bruno Fazenda, Mark R. Avis Acoustics Research Centre University of Salford Acoustics Research Centre University of Salford Email: [email protected]3.- Results: a) Time Domain method applied to Position 1 : 2.- Methods: 4.- Discussion: Absolute Relative Errors as a percentage. • Use of a Custom Rotation Cradle for the p-p probe. • Cross Laser alignment for the measurement of real positions at the receiver. • Calculation of Instantaneous Intensity in Time Domain. • Computation of Active Complex Instantaneous Intensity in Time Domain by applying the Hilbert transformH( f(t)) [1]. • Use of Short Time Fourier Transform ( STFT) with Equivalent Rectangular Bands (ERB) and Diffuseness Estimate ψ ( ) [2]. i active complex t( ) = Re 1 2 p t( ) + jH p t ( ) ⎡ ⎣ ⎤ ⎦ ( ) u t( ) − jHu t( ) ⎡ ⎣ ⎤ ⎦ ( ) ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ Precise location geometric centre of the p-p probe with the aid of a rectified Location Pin with 45º taper that acts like a mechanical pointer. _______________________________1 http://www.minalum.com.mx/ Assembly detail o f pieces of the Rotation Cradle. It was manufactured using a CNC milling machine on High grade Aluminum within tolerances of ± 1 Octagonal profile for rotating: 45º, 90º 135º, 180º, 225º and 270º fixed µm Manufactured in Minalum de México S.A. de C.V . 1 Female thread for tripod mounting b) Short Time Fourier Transform ( STFT) Method applied to Position 1: 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time[ ms ] I n s t a n t a n e o u s I n t e n s i t y i n X a x i s [ W / m 2 ] Graph of the Instantaneous Intensity arrivals at plane XZ from 0 ms to 12.4375 ms Envelope Intensity X H Envelope Intensity Z H Active instantaneous Intensity X Heyser ! Time of arrival Direct Sound = 0.208 ms Time of arrival First Reflection = 5.385 ms Outsider values Outsider values For the Direct Sound both component signals xand zhave same polarity. By simple trigonometry the modulus of the intensity yie lds a direc tion estimation of 45º. For the First Reflection both components have opposite polarity , therefore the estimated angle becomes negative: -75º 10 20 30 30 210 60 240 90 270 120 300 150 330 180 0 Graph of the Instantaneous Intensity at plane XZ (Logarithmic scale) ! Direct Sound First Reflection Less accurate estimation of First Reflection 10 20 30 30 210 60 240 90 270 120 300 150 330 180 0 Graph of the Active Complex Instantaneous Intensity at plane XZ (Logarithmic scale) ! First Reflection Direct Sound More Accurate estimation of First Reflection Time Window resolution = 2.667 ms 1 0 1 2 3 4 5 6 7 8 9 10 1 0 1 2 3 4 5 6 7 8 9 10 Mean D irection ofsoundarrivals atthe planeXZ in ERB bands Time [ ms] F r e q u e n c y [ k H z ] D i r e c t s o u n d F i r s t R e fl e c t i o n 16 Equivalent Rectangular Bands (ERB) in the frequency domain z•14 measurement positions were tested in steps of 1º, 2º and 5º covering an angle range of 30º. 1 Receiver Positions 14 12 13 11 10 9 8 7 6 5 4 2 3 Source Position x Rigid Floor in the semi-anechoic chamber Rotation cradle aligned at its geometric centre with a Laser Cross 5.- Conclusions: • T wo methods had been presented to characterise the Time of Ar rival, S trength and Direction of Arrival of Early Reflections: a) Time Domain ( TD) and b) Short Time Fourier Transform ( STFT) method. • Using these methods two variants had been compared: Instantaneous Intensity and a more accurate method based on Complex Instantaneous Intensity. • The accuracy of the angle of arrival of Direct Sound and First Reflection case had been validated using two measurement probes: a) p-p probe with a Mean error = 2.36º ±1.27ºcompared with a ST350 SoundfieldMicrophone, which has a mean error =18.79º ±0.256º(results not shown). The average err or was performed using the ERBbands ofSTFTmethod. B oth methods TD and STFTare c omplementary .
