ACOUSTIC SOURCE SEPARATION VIA PARTICLE VELOCITY VECTOR MEASUREMENT

Transcription

1 ACOUSTIC SOURCE SEPARATION VIA PARTICLE VELOCITY VECTOR MEASUREMENT Kenbu Teramoto 1, Md.Tawhidul Islam Khan 1 1 Department of Mechanical Engineering, Saga University Contents 1 Introduction 2 2 Problem Formulation 10 3 Acoustical Experiments 15 Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 1

2 1. Introduction 1.Introduction Background Indenpendent Component Analysis Objectives 2.Problem Formulation 3.Acoustical Experiments 4.Concluding Remarks Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 2

3 Acoustic Blind Source Separation Background Percussion instrument Trumpet Toronbone Tuba Harp Horn Clarinet Flute 2nd Violin Fagotto Oboe Cello Contra bass 1st Violin Viora The conductor s ears can discriminate: Sound Pressure from each instrument DOA of each instrument Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 3

4 Acoustic Blind Source Separation Background Percussion instrument Trumpet Toronbone Tuba Harp Horn Clarinet Flute 2nd Violin Fagotto Oboe Cello Contra bass 1st Violin Viora The stereo microphones can record only the mixture of Sound Pressure from all instruments cannot discriminate DOA of each instrument Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 4

5 Acoustic Blind Source Separation Background Percussion instrument Harp Horn Trumpet Clarinet Flute 2nd Violin Toronbone Fagotto Oboe Cello Tuba Contra bass 1st Violin BSS Viora Trumpet Toronbone 1st Violin The objective of BSS-microphone system to discriminate: Sound Pressure from each instrument DOA of each instrument Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 5

6 Independent Component Analysis key of Acoustic BSS Percussion instrument Trumpet Toronbone Tuba Horn Clarinet Flute Fagotto Oboe TOF Amplitude l1 c a1 Harp 2nd Violin Cello Contra bass TOF Amplitude l2 c a2 1st Violin BSS Viora Acoustic BSS Convolutive BSS: Frequency Domain ICA popular Time Domain ICA Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 6

7 Frequency Domain Independent Component Analysis g1(t) G(η) W(η) W(η) W(η) A(η) f1(t) W(η) f2(t) w1(t) w2(t) g2(t) Short-time FFT Frequency bin W 1(η1) W 2(η2) W 1(η3) W 2(η1) W 1(η2) W 2(η3) Optimize A(η) for each freqeuncy bin miss assignment IFFT W 1(ηm) w1(t) W2(ηm) w2(t) Difficulties in FDICA: Permutaion in frequency bin missing DOA Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 7

8 Spatio-Temporal Gradient Domain ICA Δg1(t) dt dt v(t) A(t) w1(t) w2(t) Δg2(t) vector sensor Optimize A(t) particle velocity vector Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 8

9 Objectives The spatio-temporal blind signal separation algorithm utilizes the linearity among the four signals: 1. the sound pressure, 2. x-directional particle velocities, 3. y-directional particle velocities, 4. z-directional particle velocities, all of which are governed by the equation of motion in order to make the convolutive blind source separation problems into the simplest instantaneous mixture problems. The directions of wave propagations can be determined with the proposed blind source separation. application tele-meeting system mobile phone hearing aid Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 9

10 2. Problem Formulation 1. Introduction 2.Problem Formulation Instantaneous linear mixture Blind Source Separation 3.Acoustical Experiments 4.Concluding Remarks Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 10

11 Instantaneous linear mixture x w1(t) z p2 p1 θ2 θ1 φ2 φ1 A =(p 1 p 2 p 3 ) φ3 w2(t) θ3 observation point p3 w3(t) Base on the wave equation of the airborne sound: f(x, y, z, t) x=y=z=0 = A ẇ1(t) ẇ 2 (t),(1) ẇ 3 (t) From the equation of motion particle velocity vector v(x, y, z, t) and the spatial gradients of the sound pressure f(x, y, z, t) satisfy: v(x, y, z, t) ρ = f(x, y, z, t), (2) t where ρ is the density of the air. y The instantenious linea mixture can be denoted as: v(x, y, z, t) ρ t x=y=z=0 = A ẇ1(t) ẇ 2 (t).(3) ẇ 3 (t) Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 11

12 Instantaneous linear mixture ρ v(x, y, z, t) t x=y=z=0 = A ẇ1(t) ẇ 2 (t). (4) ẇ 3 (t) dtρ v(x, y, z, t) t x=y=z=0 = dta ẇ1(t) ẇ 2 (t) ẇ 3 (t). (5) ρv(x, y, z, t) x=y=z=0 = A w 1(t) w 2 (t). (6) w 3 (t) Microphone which detects the particle velocity can make the convolutive cocktail-party problems into the simplest instantaneous linear mixture problems. Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 12

13 Instantaneous linear mixture ρ v(x, y, z, t) t x=y=z=0 = A ẇ1(t) ẇ 2 (t). (7) ẇ 3 (t) dtρ v(x, y, z, t) t x=y=z=0 = dta ẇ1(t) ẇ 2 (t) ẇ 3 (t). (8) ρv(x, y, z, t) x=y=z=0 = A w 1(t) w 2 (t). (9) w 3 (t) μicroflown which detects the particle velocity can make the convolutive cocktail-party problems into the simplest instantaneous linear mixture problems. Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 13

14 Blind Source Separation 1. Pre-whitening 2. Itterative Blind source separation via rotation process 3. DOA estimation vx vy vz prewhitening u1 u2 u3 rotation C(α) α u1 α u2 α u3 cost J(α) C(α) σ1 σ2 σ3 DOA amplitude W1(t) W2(t) W3(t) φ1,2,3 θ1,2,3 α=α-μ J(α) B(ψxx ψyy ψzz) Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 14

15 3. Acoustical Experiments 1.Introduction 2.Problem Formulation 3.Acoustical Experiments μicro flown Proof of Concept Model Source Signals Separated Signals 5.Concluding Remarks Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 15

16 μicro flown Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 16

17 Proof-of-Concept model left speaker 0.5m y right speaker 0.5(m) 0.5(m) φ1=2π/3(rad) φ2=π/3(rad) Digital Storage Osciloscope 3-ch Microflown x (1) signal conditioner GP-IB PC Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 17 (2)

18 Source Signals, Observed Signal No.1 No.2 source female voice, female voice, ENGLISH JAPANESE length 20s 20s arrival directions θ 1 =0(rad) θ 2 =0(rad) φ 1 =2π/3(rad) φ 2 = π/3(rad) test15-10.dat test15-20.dat (1) (2) test15x0.dat test15y0.dat (3) (4) Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 18

19 Separated Signals (1) outtest1510.dat (2) outtest1520.dat Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 19

20 DOA and SIR (rad) φ2= 2π/3 φ2 φ1= π/3 0 φ1 (1) (s) SIR(dB) 40 SIR1 (2) SIR (s) Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 20

21 4. Remarks Discussion and Remarks 1. The spatio-temporal gradient analysis has an ability to simplify the convolutive blind source separation problems into the instantaneous blind source separation over the spatio-temporal gradient space, 2. The directions of wave propagations can be determined with the proposed blind source separation. 3. Three sources can be discriminated autonomously even when they are slightly moving. Jun. 9, 2006 Dept. of Mechanical Engineering, Saga Univ., JAPAN 21