Applicatio ns of Indep endent Sub2Band Functio ns and Wavelet Analysis in Single2Channel Noisy Signal B SS :Mo del and Crucial Technique

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1 ACTA ELECTRONICA SINICA Vol. 37 No. 7 July 2009 : 1,3, 2,3, 2, 1, 4 (1., ; 2., ; 3., ;4., ) :.,;, ;, ;,. : ; ; ; ; ; : TN91117 : A : (2009) Applicatio ns of Indep endent Sub2Band Functio ns and Wavelet Analysis in Single2Channel Noisy Signal B SS :Mo del and Crucial Technique CHENG Xie2feng 1,3,TAO Ye2wei 2,3,ZHANG Shao2bai 2,ZHANG Xue2jun 1,LIU Ju 4 (1. School of electron Science and Engineering, Nanjing University of osts and Telecommunications, Nanjing, Jiangsu , China ; 2. Nanjing University of osts And Telecommunication, Nanjing, Jiangsu , China ; 3. University of Jinan, Jinan, Shandong , China ; 4. School of Information Science and Engineering, Shandong University, Jinan, Shandong , China) Abstract : Based on independent sub2band functions and wavelet analysis,the paper presents a new technique of signal pro2 cessing to accomplish blind source separation when a single2channel mixture signal in noise is given. Firstly we analyzed the compo2 sitional principle of independent sub2band function and the method how to get independent sub2band function. And combining inde2 pendent sub2band function into the single mixture signal,a single mixture signal can be transformed into a multi2dimensional vector from one2dimensional. Then we discuss the problems of second de2noising with wavelet and the order s uncertainty of data seg2 ments. The paper also presents a determine method of the number of independent sub2band function and the similar phase diagram. Through an experiment of eliminating the artifact of transient evoked otoacoustic emissions,the feasibility and effectiveness of this method have been proven. Key words : blind signal separation ;independent sub2band function ; noise ; wavelet ;independent component analysis ;transient evoked otoacoustic emissions 1 (Blind Signal Separation),.., [16],.,,, [ 9 ].,.,, ;, : ; : :(No. Y2006G03,No. Y2007G14,No. Y2007G04,No. 2006Gg ) ; (No ) ; (No. NY207139)

2 7 ::1523 ;, ;,. 2 m k, s [ s 1 ( t), s 2 ( t),, s k ( t) ] T, x [ x 1 ( t), x 2 ( t),, x m ( t) ] T, [3] : x ( t) As ( t) (1) A. E[ s i ( t 1 ), s j ( t 2 ) ] 0, i j( i, j 1, 2, k), Π t 1, t 2, E [ s i ( t ) ] 0 y [ y 1 ( t), y 2 ( t),, y k ( t) ] T, W, : y( t) Wx( t) WAs ( t) Cs ( t) (2) C WA -,. W, y ( t),. D, { dii R, i 1,2, k} ;,1,. W DA - 1,y( t), y( t),(2) : y( t) Cs ( t) Ds ( t) (3). y( t) Ds ( t), D, D,., W,,. s i ( t). N [ N 1 ( t), N 2 ( t),, N m ( t) ], N R m,: x As + N (4) (1) m k, N 0,, x As + N A x, A N s + N 1 N 2 (5) A x, A N, s + N 1,, N 2. (2) m 1, k > 1, N 0, [9,10]. k, ( ill2condi2 tioned). 2 k., [4],.,., p,,, [16]., (1) k 2,s 1 ( t) 1 ( a). s 1 ( t),s p 1 ( t), ( p 1,2, ), 1 ( b). s 1 ( t) R m,, Kullbck2Leibler,, [ b 1, b 2,, b Q ] s 1 ( t). s 1 ( t),,. 1 ( c). s 1 ( t) b q 1 ( q 1,2,, Q), 1 ( d) s 2 1. Q, C pq s 1 ( t) p q. Q,: s 1 1 s 2 1 s 1 c 11 c 12 c 1 Q c 21 c 22 c 2 Q c 1 c 2 c Q b 1 1 b 2 1 b Q 1 (6) C,s p 1 b q 1. b q 1 c pq,

3 C W C - 1, (2), s p 1, [5], W i j + 1 E x i g W i T ( j) x i - E gw i T j x i W i y (7) g, g G 1 lg cos( ay) a, 1 a 2. W i ( j) j W i, W 1, W 2,, W Q,. 312 Q Q, (6), [7,8,13]..,. (4),e 0, x As + N + e 0 (8) e 0 ( As + N), N, e 0 N. ICA [5,10,14],,,e^0 e 0. : (1) (4),, ; (2) e 0,e 0 ; (3) i 1, p i + 1,p,ICA ; (4) e 0, e 0 - e^ i 0 > e,i + 1,(3),(5). e. (5). p Q (1),m 1, k 2, x a 1 s 1 + a 2 s 2 (9) s 1 ( t), s 2 ( t),,: x p a 1 s p 1 + a 2 p s 2 p 1 p 1 p 1 (10) x p. s 1 x p,, : x p s p 11 s p 12 s p 1 Q a 2 s p 2 + a 1 s p 1 s p 11 s p 12 s p 1 Q a 2 a 1 c p1 a 1 c pq 0 c p c p c pq s p 2 b 1 1 b 2 1 b Q 1 (11) x p p, s p 1 q c pq b q 1 (6). (11), s 1 ( t),, s 1 ( t) s 2 ( t),, ICA p, ICA s^ 2. ICA s^ p 2., s^ p 2,.,,,, r( t - ),. E{ r 2 ( t - ) y 2 ( t) }. [13,14] : J ( w) 1 2 E{ 2 } + 4 ( c - E{ y2 ( t) r 2 ( t - ) } ) 2 (12) ( t) y ( t) - L b ky ( t - k), 1, c k 1,c 1, b k FIR. (12). s^ p 2. (11) ICA s^ p 1, x p - s^ p 1 x p, (2) : ( s^1 ) p W x p (13) ( s^2 ) p x p p - s^ 1,. 412 BSS,,

4 7 ::1525,,.,,. ICA f j ( i), f j + 1 ( i) : f ( i) f j ( i) u( - i + i g ) + f j + 1 ( i) u( i - i g ) f j ( i), i < i g (14) f j + 1 ( i), i > i g i g, u( i). ( a) f j + 1 ( i) f j ( i),, f j + 1 ( i) f j ( i). ( b) f j + 1 ( i) f j ( i),f j + 1 ( i) f j ( i). ( c) f j + 1 ( i) f j ( i), 180, f j + 1 ( i) f j ( i).,,y j ( i), y j + 1 ( i). 2,, db3 Coif1,,,, 2. s^ p 2 s^ p + 1 2,, ( c) p + 1,s^ 2 180, ( a), ( b), ICA,,.. ICA s^ k [15] : s^ k s^ k s k, ( k 1 2 K) (15) 414 W j, ICA ICA., (1) A, A. ICA W 1,. A,, ICA,,,, ICA, s^1 k, W 1 1. W 1 1 ICA W 2 1, ICA,,. 415 BSS. ICA [8,14], (5) N 2,. ICA N 1., ICA.. [6],(4) gx ( t) A J ( t) + [ D j ( t) + N j 1 ] (16) j 1, A J, D j, J.,,., N j 1, (16).,.,,.,, N 2, x( t).,x ( t), b 1 q,(11) x ( t).,x ( t) ICA, s^1 1, s^2 1,, s^ 1, (13) ICA s^1 2,, s^ 2. (12) s^1 2,, s^ 2., 412 6, s^1 2,, s^ 2,s^2.,s^2 N 2,, s^2, s 2. 5 a 1 a 2, a 1 (11),. a 2

5 , a 2. W s 2 1 s 22,(2) : s Wx (17) (9) : : x W - 1 s D s (18) x a 1 s 1 + a 2 s 2 a 1 s 1 + a 2 s 2 (19) f 2., 0, f 1 f 2. 2 ( d)., i ICA i. ( d 11 s 1 + d 21 s 1 ) / 2 + ( d 12 s 2 + d 22 s 2 ) / 2a 1 s 1 + a 2 s 2 : 6 a^ d ij s i i 1 2 j 1 s 2 - (21) s 1 s 2 a 1 (22) ICA.,. y ( n), s ( n), : ( y i ( n), s j ( n) ) N y i ( n) s j ( n) n 1 N n 1 y 2 i ( n) N s 2 j ( n) n 1 (23) y ( n) ks ( n), 1, k,(3),,, y i ( n) s j ( n), y i ( n) s j ( n)..,,,,. : f 1, f 2, f 1 A 1, 1, 1, f 2 A 2, 2, 2. 1 A 1 A 2, 1 2, 1 2, 45, 1, 2 ( a). 2 A 1 ka 2, 1 2, 1 2, 45 d, d k,1, 2 ( b). 3 A 1 A 2, 1 2, 1-2, 45,, 180, 1, 2 ( c).,. 4 A 1 ka 2, 1 2, 1 2,n, f 1 7 (Otoacoustic Emissions,OAEs) [11], %, db,.,,. ( Tran2 sient Evoked OAEs, TEOAEs) [12],,,.,,. TEOAEs, TEOAEs,. (Derived Nonlinear Response,DNLR) [12],,.,, DNLR,.,DNLR,TEOAEs,.

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