7 2009 7 ACTA ELECTRONICA SINICA Vol. 37 No. 7 July 2009 : 1,3, 2,3, 2, 1, 4 (1., 210001 ; 2., 210001 ; 3., 250022 ;4., 250001) :.,;, ;, ;,. : ; ; ; ; ; : TN91117 : A : 037222112 (2009) 0721522207 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 210003, China ; 2. Nanjing University of osts And Telecommunication, Nanjing, Jiangsu 210003, China ; 3. University of Jinan, Jinan, Shandong 250022, China ; 4. School of Information Science and Engineering, Shandong University, Jinan, Shandong 250001, 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 ].,.,, ;, :2008205215 ; :2008209215 :(No. Y2006G03,No. Y2007G14,No. Y2007G04,No. 2006Gg3204005) ; (No. 60872024) ; (No. NY207139)
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.,. 3 311 [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,
1524 2009. 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. 4 411 (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 p1 0 0 0 0 c p2 0 0 0 0 0 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,,
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),.. 413 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
1526 2009, 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^ 2 1 2 2 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],.. 100 %, 25-30 db,.,,. ( Tran2 sient Evoked OAEs, TEOAEs) [12],,,.,,. TEOAEs, TEOAEs,. (Derived Nonlinear Response,DNLR) [12],,.,, DNLR,.,DNLR,TEOAEs,.
7 ::1527. WINDOWS AI,,,3008000Hz, MATLAB,600 6000Hz,., 6315dB,TEOAEs, 3 (a).,teoaes,,,,, (9). s 1 ( t), s 2 ( t) TEOAEs, s ( t). TEOAEs 3 ( b),3 ( c). TEOAEs 3 ( d) (1) (2),., 180. s^2,013849, X. s^2 2 180,, s^2 019496, s^2 s 2, 4 ( d) (4),,. ( 3 ( d) 4 ( d),,. ) 8., 10, 2, 3, 4 ( a). x, b q 1 ( q 1,2,3), (11) x ( t), 411 ICA, s^1 2, s^3 2,(15) s^ 2. s^2,, s 2, 4 ( b).. 3 ( b) CNLR s 2 ( t). (22), s^2 s 2 s^1 2, s^3 2 s 1 2, s 2 2, s 3 2 4 ( d). 4 ( d) (2) s^2 2 s 2 2,,, DNLR, TEOAEs, DNLR TEOAEs,,1,,.,,. : [1 ] Nishimori, Yasunori, lumbley, Mark D. Flag manifolds for subspace ICA problems [ A ]. roceedings of IEEE International Conference on Acoustics, Speech and Signal rocessing [ C ]. Hawai,USA :CS ress,2007. 1417-1420. [2 ] Vigliano D,et al. An information theoretic approach to a novel nonlinear independent component analysis paradigm [J ]. Signal rocessing,2005,85 (5) :997-1028. [3] Cardoso J F. Blind beam forming for non2gaussian signals [J ]. IEEE roceedings,1993,18 (3) :362-370. [4 ] Cheng Xie2feng, et al. Independent sub2band functions : model and applications [ A ]. roceedings of IEEE International J oint Conference on Neural Networks [ C ]. Orlando, USA : INNS ress,2007. 1110-1114. [5 ] Qin H, Xie S. Blind separation algorithm based on covariance
1528 2009 matrix[j ]. Computer Engineeing,2003,26 (10) :36-38. [6 ] Chang S G, Yu B, Vetterli M. Adaptive wavelet threshold for image de2noising and compression [ J ]. IEEE Transactions on Image rocessing,2002,32 (9) :1532-1564. [7 ] Wold Scorss. Validatory estimation of the number of compo2 nents in factor and principal component analysis [ J ]. Tech2 nometics,1978,20 (4) :379-406. [8 ] Kundu D. Estimating the number of signals in the presence of white noise [ J ]. J oumal of statistical planning and inference, 2000,90 (5) :57-68. [9 ] Jang Gil2Jin,Lee Te2Won. A maximum likelihood approach to single2channel source separation[j ]. J ournal of Machine Learn2 ing Research,2004,28 (7-8) :1365-1392. [ 10 ] Jang Gil2Jin ; Lee Te2Won. Single2channel signal separation using time2domain basis functions [J ]. IEEE signal processing letters,2003,10 (6) :168-171. [ 11 ] Whitehead M L. Measurement of otoaconstic emissions for hearing assessment [ J ]. IEEE Engineering in Medicine and Bioogy,1994,16 (9) :210-226. [12 ] RavazTni. Evoked otoacoustic emissions nonlinearities and response interpretation [J ]. IEEE Transactions on Biomedical Engineering,1993,11 (2) :500-504. [13 ] A Salazar, J Igual. Learning hierarchies from ICA mixtures [ A ]. roceedings of IEEE International J oint Conference on Neural Networks [ C ]. Orlando,USA :INNS press,2007. 12-17. [14 ],. [J ]., 2002, 4 (30) :570-576. Liu J u, He Zhen2ya. A survey of blind source separation and blind deconvolution[j ]. Acta Electronica Sinica,2002,4 (30) : 570-576. (in Chinese) [15 ] Liu J,Iserte A,Lagunas M A. Blind separation of OSTBC signals using ICA neural networks [ J ]. IEEE International Symposium on Signal rocessing and Information Technolo2 gy,2003,23 (12) :14-17. [16 ] Cheng X F, Tao Y W. A single channel mix signal separation technique[ A ]. roceedings of IEEE International Conference : on Bioinformatics and Biomedical Engineering [ C ]. Wuhan, China :IEEE Operations Center ress,2007. 962-709.,1956 6... 6, 2, 2., 40.. E2mail :chengxf @njupt. edu. cn,1958 8... 20. E2mail :taoyw @njupt. edu. cn