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1 2005 Visualized Time Domain Signals Processing 04R3216

2 Abstract This paper introduces a new concept to extract the essential and distinct characteristics of time dependent signals. A key idea is to calculate a three-dimensional Lissajous diagram, which is able to represent the characteristics information of a time dependent signal e.g. frequency, amplitude, phase difference. Nowadays, cognition of the time domain signals has been mostly depended on the highly experienced experts. With the developments of modern high speed and reasonable priced computers, most of the works requiring human experience and skill are now planning to replace the computers, for example Artificial Intelligence and neural network studies. This means that most of things will be diagnosed by the computers in near future. Principal purpose of this paper is to develop the system, which is capable of cognizing various information by a computer. Thus, in this paper, the followings are carried out as concrete examples of signal diagnosis. First, it is carried out to cognize a position of target metallic materials and a kind of cans by means of both input and output signals of a differential magnetic sensor. Second, it is tried to cognize a kind of cans by using only one output signal. Finally, the three-dimensional Lissajous and the image cognition techniques are applied to the Biomagnetics signal recognition. In order to convert signal to image, this paper employs the Lissajous diagram. When it is taken into account the overlapped information by means of histogram, the three-dimensional Lissajous diagram can be obtained by taking one time dependent signal to the x-axis and the other time dependent signal to the y-axis. Thus, the time domain signals are converted into the three-dimensional monochrome images, which construct the signal database system. When a time domain test signal is measured, this signal is also converted into the three-dimensional image. This three-dimensional image becomes an input vector of a least square system. Least squares solution gives a composite signal as a linearly combined database signals. Extracting the most dominant element from the least squares solution reveals the cognized signal. Thus, it has been succeeded in the time domain magnetic sensor signal cognition by means of the image cognitive technology. Appendix describes a supplementary explanation about the equivalent characteristic value previously proposed. Namely, it is shown that conventional equivalent characteristic values extracted from the practical experiments are not the deterministic parameter of the system because of the noise influence accompanying the experiments. i

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5 x 1 y 1 xy

6 y Axis x Axis y Axis x Axis y Axis x Axis (a) (b) (c) y Axis 1 y Axis 1 y Axis x Axis x Axis x Axis (d) (e) (f)

7 x Axis y Axis x Axis y Axis x Axis y Axis (a) (b) (c) x Axis y Axis x Axis y Axis x Axis y Axis (d) (e) (f) [1][2] G = g( i, j) i=1,2,3,,lj=1,2,3,,l (1) 4

8 Y G Y = [ g(1,1),..., g(1, l), g(2,1), g(2, 2),..., g( ll, )] (2) n C = [ g(1,1), g(1,2),..., g(1, l), g(2,1), g(2,2),..., g(2, l), g(3,1),..., g( l, l)] 1 C = [ g(1,1), g(1,2),..., g(1, l), g(2,1), g(2,2),..., g(2, l), g(3,1),..., g( l, l)] C 2 M n = [ g(1,1), g(1,2),..., g(1, l), g(2,1), g(2,2),..., g(2, l), g(3,1),..., g( l, l)] (3) 2 1 mnci i=1 2 n(4)nmc C = c, c,., c ] (4) [ 1 2 n 1 Y (5) Y=CX (5) (5) X X=X1,X 2,, Xn (6) [3][4] (4)V1V2 Vn (6)XG(7) n X i i= 1 G = V (7) i 5

9 X (5) C C X (5) C (5) n m m>n ε = Y CX (8) (5)(9) X T 1 T ( C C ) C Y = (9) 6

10 3 (a) () (b) () (c) () (d) () (e) () (f) () (g) () (h) () (i) () 7

11 3 ()() 1 400[Hz] 1 [] [mm] 115[mm] 0.5[mm] [mm] 110[mm] 0.5[mm] (a) (b) 8

12 (a) (b) (a) () (b) () (c) () (d) () (e) () (f) () (g) () (h) () (i) () 1 9

13 (a) () (b) () (c) () (d) () (e) () (f) () (g) () (h) () (i) () 10

14 x x cii=12 92 (5) 9 64X64 64X64>9 (9)(5)[4] X Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 X 11

15 3 X X 5 12

16 5[KHz] 2[cm] [] [mm] 55[mm] 0.6[mm] 60 35[mm] 30[mm] 0.6[mm] (a) () (b) () (c) () 13

17 20[mm] 1[cm] 30 15[cm] (a) (b) (a) nothing (b) 3[cm] (c) 6[cm] (d) 9[cm] (e) 12[cm] (f) 15[cm] (g) 18[cm] (h) 21[cm] (i) 24[cm] 14

18 15[cm] 15[cm] 15[cm] (a) nothing (b) 3[cm] (c) 6[cm] (a) 1[cm] (b) 3[cm] (c) 6[cm] (d) 9[cm] (e) 12[cm] (f) 15[cm] (d) 9[cm] (e) 12[cm] (f) 15[cm] (g) 18[cm] (h) 21[cm] (i) 24[cm] (g) 18[cm] (h) 21[cm] (i) 24[cm] 5 X 15

19 (a) nothing (b) 3[cm] (c) 6[cm] (d) 9[cm] (e) 12[cm] (f) 15[cm] (g) 18[cm] (h) 21[cm] (i) 24[cm] X [cm] 30 (90 ) [] []

20 [cm] 2[cm] 25 2[cm] 25 (75 ) [] [] B

21 ()() 400[Hz] 90 3 )3 3 3 ) 18

22 a a degree degree degree degree x-axis y-axis x-axis y-axis x-axis y-axis x-axis y-axis (b) (c) 3 (b) (c)

23 (a) () (b) () (c) () (d) () (e) () (f) () (g) () (h) () (i) () 2 3 (5) Y (8)(9) (9)(5) X 20

24 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 X X X 5 3 SN SN SN 21

25 22

26 IC [2] 20 23

27 (a) (b) 9 (a) SCS-H10R (b) SCS-AD10 24

28 5.2 1 (0.04[s]) Excel Excel (a)(b) (a)(b) (a) B (b)

29 (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I X (g)(i) Excel 26

30 (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I X 27

31 5.4 (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I 8 X (g)(i) SN 28

32 (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I (a) A (b) B (c) C (d) D (e) E (f) F (g) G (h) H (i) I X 29

33 SN 30

34 3 3 3 Svip 3 31

35 Svip ECV (Equivalent Characteristic Value) [5]ECV ECV ECV 3 ECV [6] R L V A.1 A.1 n t (a1) i n t = i + i i ε λ t ( n+ ) t [ ( n 1) t ( n+ 1) t ] 1 (a1) R-L ECV (a2) 1 i i ( ) ( ) i n 1 t i n+ t n t ( n+ 1) t λ = ln (a2) t 1 A.(a2) ECV A.2 ECV 32

36 A.1 R-L (a) A.2 A.1 ECV (b) ECV ECV ECV ECV [7] R-L [Hz] R=98.23[Ω]ωL=2.677[Ω] A.3(a) ECV A.4 ECV Log 1000 A.3(b) ECV A.5 A.5 33

37 (a) A.3 R-L (b) (a) A.4 A.3(a) ECV (b) (a) A.5 A.3(b) ECV (b) A.6 A.6 ECV A.7 A.8 A.9 ECV ECV ECV 34

38 (a) (b) (c) () (d) A.6 (R-L ) () (a) (b) (c) () (d) A.7 A.6 ECV (a) (b) (c) () (d) A.8 A.6 ECV (a) (b) (c) () (d) A.9 A.6 ECV R-L R-L R-C 35

39 ECV [6] A.10 A.10 Svip ECV (Equivalent Characteristic Value) ECV ECV [5] ECV 36

40 B [cm]1[cm] B.1 B.1 2[cm] 5[KHz] B.1 1[cm] [] [mm] 55[mm] 0.6[mm] 60 16[mm] 30[mm] 0.6[mm] B.1 B.2 10[mm] 1[cm] 30 15[cm] (a) () (b) () (c) () B.2 1[cm] 37

41 3.2 B.2 B.1 B B.3 B.2 1[cm] 30 (90 ) [] [] B.3 1[cm] 20 (60 ) [] [] [cm] 3.2 B [cm] 1[cm] 2[cm] 1[cm] B.4 2[cm] B.5 1[cm] 2[cm] B.6 38

42 B.4 1[cm] 20 (60 ) [] [] B.5 2[cm] 25 (75 ) [] [] B.6 1[cm]+2[cm] 1[cm]+2[cm] (135 ) [] 33 [] 76 B B.4 B.2 2[cm] B

43 [1] vol.24 No.1pp [2] [3] Mathematica 1996 [4] H.Takahashi,S.Hayano,Y.SaitoVisualization of the Currents on The Printed Circuit Boards IEEE Visualization 1999, Late Breaking Hot Topics, pp.37-40,oct [5] vol.33no.1pp [6] -- MAG [7]

44 No.1pp No.1pp ( 2005) No.2pp MAG

45 42

Abstract This paper concerns with a method of dynamic image cognition. Our image cognition method has two distinguished features. One is that the imag

Abstract This paper concerns with a method of dynamic image cognition. Our image cognition method has two distinguished features. One is that the imag 2004 RGB A STUDY OF RGB COLOR INFORMATION AND ITS APPLICATION 03R3237 Abstract This paper concerns with a method of dynamic image cognition. Our image cognition method has two distinguished features. One

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