(DFT) 009 DFT: Discrete Fourier Transform N x[n] DFT N 1 X[k] = x[n]wn kn, k = 0, 1,, N 1 (6 ) n=0 1) W N = e j π N W N twidd
|
|
|
- こうき うづき
- 7 years ago
- Views:
Transcription
1 (DFT) 6-1 DFT 6- DFT FFT 6-3 DFT c 011 1/(0)
2 (DFT) 009 DFT: Discrete Fourier Transform N x[n] DFT N 1 X[k] = x[n]wn kn, k = 0, 1,, N 1 (6 ) n=0 1) W N = e j π N W N twiddle factor DFT X[k] x[n] N x[n] DFT X[k] W N x[n] = 1 N N 1 X[k]WN nk, n = 0, 1,, N 1 (6 ) k=0 X[k] x[n] DFT IDFT: Inverse DFT 6 DFT N 1 x = [x(0), x(1),, x(n 1)] T X = [X(0), X(1),, X(N 1)] T DFT IDFT X = W N x x = 1 N W N X (6 3) (6 4) W N N N k n [W N ] k,n = WN kn W N W N W N = NI N DFT x[n] N DFS: Discrete Fourier Series 1) x[n] DTFT: Discrete-Time Fourier Transform 1 N X[k] = X(e jω ) ω= π N k 1) DFT N DTFT c 011 /(0)
![x = [x(0), x(1),, x(n 1)] T X = [X(0), X(1),, X(N 1)] T DFT IDFT X = W N x x = 1 N W N X (6 3) (6 4) W N N N k n [W N ] k,n = WN kn W N W N W N =](/docs-images/42/23059160/images/page_2.jpg "NI 6--1--3 N DFT x[n] N DFS: Discrete Fourier Series 1) x[n] DTFT: Discrete-Time Fourier Transform 1 N X[k] = X(e jω ) ω= π N k 1) DFT N DTFT c 011")
3 6 DFT X[k], X 1 [k], X [k] x[n], x 1 [n], x [n] DFT a, b (( )) N N R{ } I{ } R N N DFT N ax 1 [n] + bx [n] ax 1 [k] + bx [k] X[n] Nx[(( k)) N ] x[((n m)) N ] WN kmx[k] W N lnx[n] N 1 X[((k l)) N] x 1 [m]x [((n m)) N ] X 1 [k]x [k] m=0 x 1 [n]x [n] 1 N 1 X 1 [l]x [((l k)) N ] N x [n] X [(( k)) N ] x [(( n)) N ] X [k] R {x[n]} X ep [k] = 1 {X[((k)) N] + X [(( k)) N ]} ji {x[n]} X op [k] = 1 {X[((k)) N] X [(( k)) N ]} x ep [k] = 1 {x[n] + x [(( n)) N ]} R {X[k]} x op [n] = 1 {x[n] x [(( n)) N ]} ji {X[k]} X[k] = X [(( k)) N ] R {X[k]} = R {X[(( k)) N ]} x[n] R ji {X[k]} = ji {X[(( k)) N ]} X[k] = X[(( k)) N ] X[k] = X[(( k)) N ] l=0 1) A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, nd ed, Prentice Hall, c 011 3/(0)
![X op [k] = 1 {X[((k)) N] X [(( k)) N ]} x ep [k] = 1 {x[n] + x [(( n)) N ]} R {X[k]} x op [n] = 1 {x[n] x [(( n)) N ]} ji {X[k]} X[k] = X [(( k)) N ] R {X[k]} = R {X[(( k)) N ]} x[n] R ji](/docs-images/42/23059160/images/page_3.jpg "{X[k]} = ji {X[(( k)) N ]} X[k] = X[(( k)) N ] X[k] = X[(( k)) N ] l=0 1) A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, nd ed, Prentice Hall, 1999.")
4 (FFT) 009 DFT DFT DFT FFT: Fast Fourier Transform N N DFT (N/) 1 X[k] = x[r]wn kr r=0 (N/) 1 + r=0 x[r + 1]W kr+k N = G[k] + W k N H[k], k = 0, 1,, N 1 (6 5) G[k] = (N/) 1 r=0 x[r]w kr N/ H[k] = (N/) 1 r=0 x[r + 1]W kr N/ WN = W N/ X[k] x[r] N/ DFT G[k] x[r + 1] N/ DFT H[k] WN k W N = e j π N W kn N = Wk(n+N) N = W (k+n)n N (6 6) G[k + N/] = G[k], H[k + N/] = H[k] (6 3) N N(N 1) (6 5) (N + N /) N / N > N (6 5) (6 5) FFT FFT(FFT: Decimation-in-time FFT) 1) (6 5) N DFT k = 0, 1,, N/ 1 X[k] = G[k] + W k N H[k], (6 7) X[k + N/] = G[k + N/] + W k+n/ N H[k + N/] = G[k] + W N/ N Wk NH[k] (6 8) W N/ N = e j π N N = e jπ = 1 WN k N = 8 = 3 FFT 3 N = v v 1 1 N = v c 011 4/(0)
![G[k + N/] = G[k], H[k + N/] = H[k] (6 3) N N(N 1) (6 5) (N + N /) N / N > N (6 5) (6 5) FFT FFT(FFT: Decimation-in-time FFT) 1) 6---- (6 5) N DFT k = 0, 1,, N/ 1 X[k] = G[k] + W](/docs-images/42/23059160/images/page_4.jpg "k N H[k], (6 7) X[k + N/] = G[k + N/] + W k+n/ N H[k + N/] = G[k] + W N/ N Wk NH[k] (6 8) W N/ N = e j π N N = e jπ = 1 WN k 1 6 6 6 N = 8 = 3 FFT 3 N = v v 1 1 N = v c 011")
5 G[k] X[k] H[k] W k N X[k + N/] 6 x[0] X[0] x[4] W 0 8 X[1] x[] W 0 8 X[] x[6] W 0 8 W 8 X[3] x[1] W 0 8 X[4] x[5] W 0 8 W 1 8 X[5] x[3] W 0 8 W 8 X[6] x[7] W 0 8 W 8 W 3 8 X[7] 6 FFT (N = 8 = 3 ) FFT 1 N/ v vn/ = (N/) log N ( N/) log N N log N N DFT FFT FFT Decimation-in-frequency FFT 1) FFT x[n] DFT X[k] DFT FFT Split-Radix FFT ) DFT N N prime factor FFT 1) DFT real-valued FFT, 3) prune 4) Winograd Winograd DFT 1) 1) A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, nd ed, Prentice Hall, c 011 5/(0)
![Decimation-in-frequency FFT 1) FFT x[n] DFT X[k] DFT FFT Split-Radix FFT ) DFT N N prime factor FFT 1) DFT real-valued FFT, 3) prune 4)](/docs-images/42/23059160/images/page_5.jpg "Winograd Winograd DFT 1) 1) A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, nd ed, Prentice Hall, 1999.")
6 ) S.G. Johnson and M. Frigo, A Modified Split-Radix FFT With Fewer Arithmetic Operations, IEEE Trans. on SP, vol.55, no.1, pp , ) H. Sorensen, D. Jones, M. Heideman, and C. Burrus, Real-valued Fast Fourier Transform Algorithms, IEEE Trans. on ASSP, vol.35, no.6, pp , ) H. Sorensen and C. Burrus, Efficient Computation of The DFT with Only A Subset of Input or Output Points, IEEE Trans. on SP, vol.41, no.3, pp , c 011 6/(0)
7 (Circular Convolution) 009 FFT DFT DFT N x 1 [n] x [n] x 1 [n], x [n] N 1 x 3 [n] = x 1 [n] N x [n] x 1 [((m)) N ]x [((n m)) N ], n = 0, 1,, N 1 m=0 1) (( )) N N x 1 [n], x [n] N x 3 [n] = x [n] N x 1 [n] (6 9) DFT x 3 [n] N N DFT N 1 X 3 [k] = x 3 [n]wn kn N 1 = m=0 N 1 = m=0 n=0 N 1 x 1 [((m)) N ]WN km N 1 x 1 [m]wn km l=0 N 1 N 1 = n=0 n=0 m=0 x 1 [((m)) N ]x [((n m)) N ]W kn N x [((n m)) N ]W k(n m) N x [l]wn kl, k = 0, 1,, N 1 ( W N ) (6 0) x 1 [n], x [n] N DFT X 1 [k], X [k] X 3 [k] = X 1 [k]x [k] DFT X 1 [k]x [k] = X [k]x 1 [k] x 1 [n], x [n] L, M x 1 [n] = 0, x [n] = 0, n < 0 N L + M 1 x [((l)) N ] = x [l] = 0, (L 1) l 1 x 1 [n], x [n] N 0 n < N L 1 L 1 x 1 [n] N x [n] = x 1 [m]x [((n m)) N ] = x 1 [m]x [n m] = x 1 [n] x [n] m=0 m=0 (6 1) DFT FIR 1) A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, nd ed, Prentice Hall, c 011 7/(0)
![[((n m)) N ]W kn N x [((n m)) N ]W k(n m) N x [l]wn kl, k = 0, 1,, N 1 ( W N ) (6 0) x 1 [n], x [n] N DFT X 1 [k], X [k] X 3 [k] = X 1 [k]x [k] DFT X 1 [k]x [k] = X [k]x 1 [k] 6--3--3 x 1 [n], x [n]](/docs-images/42/23059160/images/page_7.jpg "L, M x 1 [n] = 0, x [n] = 0, n < 0 N L + M 1 x [((l)) N ] = x [l] = 0, (L 1) l 1 x 1 [n], x [n] N 0 n < N L 1 L 1 x 1 [n] N x [n] = x 1 [m]x [((n m)) N ] = x 1 [m]x [n m] = x 1 [n] x [n] m=0 m=0 (6")
8 ) MRA Multi-Resolution Analysis V j j, k Z j, k 1. V j V j j Z V j = {0} j Z V j = L (R) 4. f (t) V j f (t) V j+1 5. f (t) V j f (t j k) V j 6. φ(t) V 0 {φ(t k) k Z} V 0 4 j j 1 V j+1 = V j W j, V j W j (6 ) W j L (R) = j Z W j (6 3) W 0 ψ(t k) V 0 φ(t k) MRA MRA 1) S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Patt. Anal. Mach. Intell., vol.11, no.7, pp , c 011 8/(0)
9 PRFB {A(z), B(z)} {P(z), Q(z)} 1,, 3, 4, 5) x(n) A(z) x(n) B(z) c(n) P(z) y 1 (n) d(n) Q(z) y (n) A(z)P(z) + A( z)p( z) =, B(z) = P( z), Q(z) = A( z), (6 4) (6 5) (6 6) π z = z e j (6 7) y(n) = y 1 (n) + y (n) (6 8) y(n) x(n l) (6 9) PRFB l (6 4) A(z)P(z) A(z), P(z) PRFB A(z)P(z) p(n) q(n) 1 A 0 (z) = z 1 5, 6), P 0 (z) = 1 A 1 (z) = A 0 (z) + P 0 ( z)s (z ), (6 0) P 1 (z) = P 0 (z), (6 ) S (z) = 1 ( z + 9z z ) 16 (6 ) c 011 9/(0)
10 A 1 (z) P 1 (z) A 1 (z) z A 1 (z) A 1 (z) = 1 ( z 4 + 0z 3 + 9z + 16z 1 + 9z 0 + 0z 1 z ) (6 3) 16 P 1 (z) = 1 A 1 (z) z A 1 (z) (6 4) A 1 (z) = 1 ( z 3 + 0z + 9z z 1 + 0z z 3) (6 5) 16 H(z) = A 1 (z)p 1 (z) H(z) + H( z) H(z) + H( z) = (6 6) H(z) ( 3 A n ( 1) = 0 A n (z) ) z 1 A n+1 (z) = 1 P n+1 (z) = 1 A n (z) ( 1 + z 1 ), (6 7) ( 1 + z 1 ) P n (z) (6 8) A (z), P (z) A (z) = 1 ( z + z 1 + 8z 0 + 8z 1 + z z 3) 8 (6 9) P (z) = 1 ( ) 1 + z 1 (6 30) 4 A 3 (z), P 3 (z) A 3 (z) = 1 4 P 3 (z) = 1 4 ( z 1 + z 0 + 6z 1 + z z 3) (6 31) ( ) 1 + z 1 1 ( = 1 + z 1 + z ) (6 3) 4 c /(0)
11 5 A 4 (z), P 4 (z) A 4 (z) = 1 P 4 (z) = 1 8 ( z 0 + 3z 1 + 3z z 3) (6 33) ( ) 1 + z ( = 1 + 3z 1 + 3z + z 3) (6 34) 8 6 A 5 (z), P 5 (z) A 5 (z) = z 1 + 4z z 3 P 5 (z) = 1 16 (6 35) ( ) 1 + z ( = 1 + 4z 1 + 6z + 4z 3 + z 4) (6 36) 16 7 A 5 (z) A 5 (z) = z ( z + 3 ) ( z 3 ) (6 37) 8 H(z) = A 5 (z)p 5 (z) H(z) = A(z)P(z) P(z) = 1 ( ) 1 + z 1 { ( ) } z 1, 4 (6 38) A(z) = 1 ( ) 1 + z 1 { ( ) } z 1 z 3. 8 (6 39) ( 1 3 ) z 1 = z ( ) z = z ( ) ( z + 3 ), ( ) z 1 = z ( ) z = z ( ) ( z 3 ). 3 9 P(z) z z p(n) p(n) c /(0)
12 P(z) = 1 4 { ( ) + ( ) z 1 + ( 3 3 ) z + ( 1 3 ) z 3} (6 40) = p(0) + p(1)z 1 + p()z + p(3)z 3 (6 41) 0 lowpass p(n) highpass q(n) = ( 1) n p(3 n), n = 0, 1,, 3 q(0) 3 p(n k)q(n) = ( q(1) p(0) p(1) p() p(3) ) (6 4) q() n=0 q(3) k highpass Q(z) Q(z) = q(0) + q(1)z 1 + q()z + q(3)z 3 (6 43) = p(3) p()z 1 + p(1)z p(0)z 3 (6 44) = 1 4 { ( 1 3 ) ( 3 3 ) z 1 + ( ) z ( ) z 3} (6 45) k q(0) 3 p(n)q(n) = ( p(0) p(1) p() p(3) ) q(1) = 0 q() n=0 q(3) (6 46) q(0) 3 p(n )q(n) = ( 0 0 p(0) p(1) ) q(1) = 0 q() n=0 q(3) (6 47) q(0) 3 p(n + )q(n) = ( p() p(3) 0 0 ) q(1) = 0 q() n=0 q(3) (6 48) k = 0, ±1 k {p(n)} {q(n)} {p(n)} {q(n)} p(n), q(n) 4 7) c 011 1/(0)
13 3 p(n k)p(n) = δ(k), for k n=0 3 q(n k)q(n) = δ(k), for k n=0 1, for k = 0 δ(k) = 0, (6 49) (6 50) lowpass filter {p(n)} highpass filter {q(n)} 7, 4 8) 5/3 (6 31) (6 3) 4 p 0 p 1 p p p 0 p 1 p p L = (6 51) p 0 p 1 p p 3 p p p 0 p 1 p 3 p p 1 p p 3 p p 1 p H = (6 5) p 3 p p 1 p 0 p 1 p p 3 p T = 1 L H TT t = I T (6 46) TT t 5 TT t /1 9, 10) x(t) coarse c(t) detail d(t) c /(0)
14 c(t) = x(t) d(t) = x(t + 1) (6 53) (6 54) A(z) P(z) 1/1 1 = x(t) floor + 1 (dc gain) 1 55 d(t) JPEG000 / d(t) d(t) c(t) 3 /3 (6 55) = x(t + 1) x(t)) (6 56) c(t) + c(t + 1) d(t) d(t) x(t) + x(t + ) = x(t + 1) 4 / ( Haar ) (6 57) (6 58) d(t) d(t) c(t) (6 59) = x(t + 1) x(t) (6 60) c(t) c(t) + 1 d(t) = x(t) + 5 /6 ( S+P 11) ) x(t + 1) x(t) x(t) + x(t + 1) (6 61) (6 6) c /(0)
15 d(t) d(t) c(t) (6 63) = x(t + 1) x(t) (6 64) c(t) c(t) + d(t) (6 65) x(t + 1) x(t) x(t) + x(t + 1) = x(t) + (6 66) c(t) c(t + ) d(t) d(t + 1) (6 67) x(t) + x(t + 1) x(t + 4) + x(t + 5) x(t + 3) x(t + ) (6 68) 11) S+P x(t) + x(t + 1) c(t) c(t) + 4x(t + ) 4x(t + 3) + c(t + ) d(t) 4 (6 69) (6 70). d(t) d(t) d(t) d(t) + c(t) (6 71) (6 7) c(t) c(t) d(t) (6 73) c(t) c(t + ) d(t) d(t + 1) (6 74) { 1, 1, 8, 8, 1, 1} S+P { 1, 1, 8, 8, 1, 1} S +P 6 5/3 ( 5/3-SSKF, 1) CDF(,)) JPEG000/Lossless c(t) + c(t + 1) d(t) d(t) (6 75) x(t) + x(t + 1) x(t + ) (6 76) d(t) + d(t + 1) c(t) c(t + 1) (6 77) x(t) + x(t + 1) + 6x(t + ) + x(t + 3) x(t + 4) 8 (6 78) c /(0)
16 13) 7 5/11 5/3 (,) c(t) + c(t + 1) d(t) d(t) (6 79) x(t) + x(t + 1) x(t + ) (6 80) d(t) + d(t + 1) c(t) c(t + 1) (6 81) x(t) + x(t + 1) + 6x(t + ) + x(t + 3) x(t + 4) 8 (6 8) c(t ) c(t 1) c(t) + c(t + 1) d(t) d(t) (6 83) x(t 4) + x(t 3) + 7x(t ) 136x(t) 56 56x(t + 1) 136x(t + ) + 7x(t + 4) + x(t + 5) x(t + 6) + 56 (6 84) Calderbank, Daubechies, and Sweldens 10) (4, ) 5/ /7 (transform gain) 5/3 14) (4, ) c(t 1) + 9c(t) + 9c(t + 1) c(t + ) d(t) d(t) (6 85) x(t ) 9x(t) + 16x(t + 1) 9x(t + ) + x(t + 4) (6 86) 16 d(t 1) + d(t) c(t) c(t) (6 87) x(t 4) 8x(t ) + 16x(t 1) 64 46x(t) + 16x(t + 1) 8x(t + ) + x(t + 4) + (6 88) 64 c /(0)
17 c(t) = x(t) d(t) = x(t 1) (6 89) (6 90) c(t + 1) + 9c(t) + 9c(t 1) c(t ) d(t) d(t) (6 91) x(t + ) 9x(t) + 16x(t 1) 9x(t ) + x(t 4) (6 9) 16 d(t + 1) + d(t) c(t) c(t) (6 93) x(t + 4) 8x(t + ) + 16x(t + 1) 64 46x(t) + 16x(t 1) 8x(t ) + x(t 4) + (6 94) 64 9 d(t) { } { } d(t) c(t l) c(t) { } { } c(t) + d(t l) Sweldens 9) (6 ) S (z) FIR in-place 0 4/4 ( CDF(3,1)) ) a k = A(1) = 3 k b k = B( 1) = 3 k (6 95) (6 96) a k, b k lowpass filter highpass filter c /(0)
18 A(z) B(z) c(t) c(t) d(t) 3 (6 97) x(t + 1) x(t) 3 (6 98) 3c(t) 9c(t + 1) d(t) d(t) 8 (6 99) 3x(t) x(t + 1) 9x(t + ) + 3x(t + 3) x(t + 1) 8 (6 00) 3x(t) + 9x(t + 1) 9x(t + ) + 3x(t + 3) = 8 (6 01) c(t) c(t + 1) d(t) x(t) + 3x(t + 1) + 3x(t + ) x(t + 3) 6 (6 0) (6 03) 11 m/n m A(z) n P(z) 5/3 3/5 CDF (m, n) ( ) 1 + z 1 m A(z) = A (z), (6 04) ( ) 1 + z 1 n P(z) = P (z) (6 05) z = 1 Admissibility A(z), P(z) z = LOT (lapped orthogonal transforms) DCT QMF z = 1 (checker-board artifact) LL, HL, LH, HH 4 quadrature-mirror filter bank, c /(0)
19 6 3 8) 5 Haar 7) 1/1 15) 16, 17) 1) D. Esteban and C. Galand, Application of quadrature mirror filters to split-band voice coding schemes, Proc. IEEE ISCAS 1977, vol., pp , ) M.J.T. Smith and T.P. Barnwell, Exact reconstruction techniques for tree-structured subband coders, IEEE Trans. ASSP, vol.34, pp , ) M. Vetterli, Filter banks allowing perfect reconstruction, Signal Proc., vol.10, pp.19-44, ) P.P. Vaidyanathan, Theory and design of M channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect reconstruction property, IEEE Trans. ASSP, vol.35, pp , ) G. Strang and T.Q. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, MA, c /(0)
20 6) H. Kiya, M. Yae, and M. Iwahashi, A linear-phase two-channel filter bank allowing perfect reconstruction, Proc. IEEE ISCAS, pp , ) I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., vol.41, pp , ) I. Daubechies, Ten Lectures on Wavelets, SIAM, ) W. Sweldens, The lifting scheme: A new philosophy in biorthogonal wavelet constructions, Proc. SPIE, vol.569, pp.68-79, ) A. Calderbank, I. Daubechies, W. Sweldens, and B.L. Yeo, Lossless image compression using integer to integer wavelet transforms, Proc. IEEE Int. Conf. on Image Proc., Washington, DC, USA, vol.1 of 3, pp , ) A. Said and W.A. Pearlman, An image multiresolution representation for lossless and lossy compression, IEEE Trans. Image Proc., vol.5, pp , ) D. Le Gall and A. Tabatabai, Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques, Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., New York, vol., pp , ) M.D. Adams and F. Kossentini, Reversible integer-to-integer wavelet transforms for image compression: performance evaluation, IEEE Trans. Image Proc., vol.9, no.6, pp , ) K. Shinoda, H. Kikuchi, and S. Muramatsu, Lossless-by-lossy coding for scalable lossless image compression, IEICE Trans. Fundamentals, vol.e91-a, no.11, pp , ),,,, ECG,, vol.j79-d-ii, no.8, pp , ),, Total-Variation,, vol.41, no.11, pp , ) T. Saito, N. Fujii, and T. Komatsu, Iterative soft color-shrinkage for color-image denoising, Proc. IEEE ICIP 009, Cairo, 009. c 011 0/(0)
(5 B m e i 2π T mt m m B m e i 2π T mt m m B m e i 2π T mt B m (m < 0 C m m (6 (7 (5 g(t C 0 + m C m e i 2π T mt (7 C m e i 2π T mt + m m C m e i 2π T
2.6 FFT(Fast Fourier Transform 2.6. T g(t g(t 2 a 0 + { a m b m 2 T T 0 2 T T 0 (a m cos( 2π T mt + b m sin( 2π mt ( T m 2π g(t cos( T mtdt m 0,, 2,... 2π g(t sin( T mtdt m, 2, 3... (2 g(t T 0 < t < T
main.dvi
3 Discrete Fourie Transform: DFT DFT 3.1 3.1.1 x(n) X(e jω ) X(e jω )= x(n)e jωnt (3.1) n= X(e jω ) N X(k) ωt f 2π f s N X(k) =X(e j2πk/n )= x(n)e j2πnk/n, k N 1 (3.2) n= X(k) δ X(e jω )= X(k)δ(ωT 2πk
Wavelet HSI / [1] JPEG2000 9/7Wavelet [2][6] 2:1 9/7Wavelet Wavelet 80 Wavelet i
![Wavelet HSI / [1] JPEG2000 9/7Wavelet [2][6] 2:1 9/7Wavelet Wavelet 80 Wavelet i](/thumbs/91/105321936.jpg "Wavelet HSI / [1] JPEG2000 9/7Wavelet [2][6] 2:1 9/7Wavelet Wavelet 80 Wavelet i")
17 Wavelet Image Enhancement by Wavelet Transform 1060326 2006 3 10 Wavelet HSI / [1] JPEG2000 9/7Wavelet [2][6] 2:1 9/7Wavelet Wavelet 80 Wavelet i Abstract Image Enhancement by Wavelet Transform Yuichi
h(n) x(n) s(n) S (ω) = H(ω)X(ω) (5 1) H(ω) H(ω) = F[h(n)] (5 2) F X(ω) x(n) X(ω) = F[x(n)] (5 3) S (ω) s(n) S (ω) = F[s(n)] (5
![h(n) x(n) s(n) S (ω) = H(ω)X(ω) (5 1) H(ω) H(ω) = F[h(n)] (5 2) F X(ω) x(n) X(ω) = F[x(n)] (5 3) S (ω) s(n) S (ω) = F[s(n)] (5](/thumbs/91/106545489.jpg "h(n) x(n) s(n) S (ω) = H(ω)X(ω) (5 1) H(ω) H(ω) = F[h(n)] (5 2) F X(ω) x(n) X(ω) = F[x(n)] (5 3) S (ω) s(n) S (ω) = F[s(n)] (5")
1 -- 5 5 2011 2 1940 N. Wiener FFT 5-1 5-2 Norbert Wiener 1894 1912 MIT c 2011 1/(12) 1 -- 5 -- 5 5--1 2008 3 h(n) x(n) s(n) S (ω) = H(ω)X(ω) (5 1) H(ω) H(ω) = F[h(n)] (5 2) F X(ω) x(n) X(ω) = F[x(n)]
p03.dvi
3 : 1 ( ). (.. ), : 2 (1, 2 ),,, etc... 1, III ( ) ( ). : 3 ,., III. : 4 ,Weierstrass : Rudin, Principles of Mathematical Analysis, 3/e, McGraw-Hil, 1976.. Weierstrass (Stone-Weierstrass, ),,. : 5 2π f
2 DWT DWT (Complex Discrete Wavelet Transform CDWT) [ ] DWT Hilbert ( ) DWT DWT [8] CDWT Hilbert 1/2 2 Hilbert [9] CDWT [10] Meyer (Perfect Tran
![2 DWT DWT (Complex Discrete Wavelet Transform CDWT) [ ] DWT Hilbert ( ) DWT DWT [8] CDWT Hilbert 1/2 2 Hilbert [9] CDWT [10] Meyer (Perfect Tran](/thumbs/92/108391319.jpg "2 DWT DWT (Complex Discrete Wavelet Transform CDWT) [ ] DWT Hilbert ( ) DWT DWT [8] CDWT Hilbert 1/2 2 Hilbert [9] CDWT [10] Meyer (Perfect Tran")
1622 2009 1-17 1 Translation-Invariance Complex Discrete Wavelet Transform (Zhong Zhang) * (Hiroshi Toda) * * (Toyohashi University of Technology) 1 (Discrete Wavelet Transform DWT) DWT Mallat[1] (Multi
main.dvi
4 DFT DFT Fast Fourier Transform: FFT 4.1 DFT IDFT X(k) = 1 n=0 x(n)e j2πkn (4.1) 1 x(n) = 1 X(k)e j2πkn (4.2) k=0 x(n) X(k) DFT 2 ( 1) 2 4 2 2(2 1) 2 O( 2 ) 4.2 FFT 4.2.1 radix2 FFT 1 (4.1) 86 4. X(0)
1 -- 9 -- 3 3--1 LMS NLMS 2009 2 LMS Least Mean Square LMS Normalized LMS NLMS 3--1--1 3 1 AD 3 1 h(n) y(n) d(n) FIR w(n) n = 0, 1,, N 1 N N = 2 3--1-
1 -- 9 3 2009 2 LMS NLMS RLS FIR IIR 3-1 3-2 3-3 3-4 c 2011 1/(13) 1 -- 9 -- 3 3--1 LMS NLMS 2009 2 LMS Least Mean Square LMS Normalized LMS NLMS 3--1--1 3 1 AD 3 1 h(n) y(n) d(n) FIR w(n) n = 0, 1,, N
untitled
17 2 Realization on the Direct Two-dimensional Wavelet Transform 1060341 2006 3 10 2 JPEG JPEG2000 [1] X-Y X 1 Y 1 VGA 1 1MBte LSI LSI 2 2 5/3 [2][3] 2 5/3 9/7 7 7 N X M Y 32N M 10N M X-Y 9/7 4 1.67 1
untitled
On a Correlation-based Scheme of Digital Watermarking for Images Exploiting 2-D LOT Hiromu KODA and Kyousuke KAMINUSI Abstract In this paper, we propose a correlation based scheme of digital watermarking
数値計算：フーリエ変換
( ) 1 / 72 1 8 2 3 4 ( ) 2 / 72 ( ) 3 / 72 ( ) 4 / 72 ( ) 5 / 72 sample.m Fs = 1000; T = 1/Fs; L = 1000; t = (0:L-1)*T; % Sampling frequency % Sample time % Length of signal % Time vector y=1+0.7*sin(2*pi*50*t)+sin(2*pi*120*t)+2*randn(size(t));
ds2.dvi
1 Fourier 2 : Fourier s(t) Fourier S(!) = s(t) = 1 s(t)e j!t dt (1) S(!)e j!t d! (2) 1 1 s(t) S(!) S(!) =S Λ (!) Λ js T (!)j 2 P (!) = lim T!1 T S T (!) = T=2 T=2 (3) s(t)e j!t dt (4) T P (!) Fourier P
さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a
![さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a](/thumbs/97/131721994.jpg "さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a")
φ + 5 2 φ : φ [ ] a [ ] a : b a b b(a + b) b a 2 a 2 b(a + b). b 2 ( a b ) 2 a b + a/b X 2 X 0 a/b > 0 2 a b + 5 2 φ φ : 2 5 5 [ ] [ ] x x x : x : x x : x x : x x 2 x 2 x 0 x ± 5 2 x x φ : φ 2 : φ ( )
arma dvi
ARMA 007/05/0 Rev.0 007/05/ Rev.0 007/07/7 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3.3 : : : :
CPU Levels in the memory hierarchy Level 1 Level 2... Increasing distance from the CPU in access time Level n Size of the memory at each level 1: 2.2
FFT 1 Fourier fast Fourier transform FFT FFT FFT 1 FFT FFT 2 Fourier 2.1 Fourier FFT Fourier discrete Fourier transform DFT DFT n 1 y k = j=0 x j ω jk n, 0 k n 1 (1) x j y k ω n = e 2πi/n i = 1 (1) n DFT
II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
![II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2](/thumbs/101/149159646.jpg "II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2")
II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
GSP_SITA2017_web.key
ytnk@cc.tuat.ac.jp 25 DFT spectrum 2 15 1 5 1 2 3 Frequency index 4 5 25 15 1 DFT spectrum 2 5 1 2 3 Frequency index 4 5 .8 GFT spectrum.6 1.4.2 5 1 15 Graph frequency (eigenvalue) 1 GFT
pp d 2 * Hz Hz 3 10 db Wind-induced noise, Noise reduction, Microphone array, Beamforming 1
72 12 2016 pp. 739 748 739 43.60.+d 2 * 1 2 2 3 2 125 Hz 0.3 0.8 2 125 Hz 3 10 db Wind-induced noise, Noise reduction, Microphone array, Beamforming 1. 1.1 PSS [1] [2 4] 2 Wind-induced noise reduction
211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
H(ω) = ( G H (ω)g(ω) ) 1 G H (ω) (6) 2 H 11 (ω) H 1N (ω) H(ω)= (2) H M1 (ω) H MN (ω) [ X(ω)= X 1 (ω) X 2 (ω) X N (ω) ] T (3)
![H(ω) = ( G H (ω)g(ω) ) 1 G H (ω) (6) 2 H 11 (ω) H 1N (ω) H(ω)= (2) H M1 (ω) H MN (ω) [ X(ω)= X 1 (ω) X 2 (ω) X N (ω) ] T (3)](/thumbs/92/108069141.jpg "H(ω) = ( G H (ω)g(ω) ) 1 G H (ω) (6) 2 H 11 (ω) H 1N (ω) H(ω)= (2) H M1 (ω) H MN (ω) [ X(ω)= X 1 (ω) X 2 (ω) X N (ω) ] T (3)")
72 12 2016 pp. 777 782 777 * 43.60.Pt; 43.38.Md; 43.60.Sx 1. 1 2 [1 8] Flexible acoustic interface based on 3D sound reproduction. Yosuke Tatekura (Shizuoka University, Hamamatsu, 432 8561) 2. 2.1 3 M
0A_SeibutsuJyoho-RF.ppt
A ON-Center OFF-Center DeAngelis, Ohzawa, Freeman 1995 Nobel Prize 1981: Physiology and Medicine D.H. Hubel and T.N. Wiesel T.N. Wiesel D.H. Hubel V1/V2: (spikes) Display? Amplifiers and Filters V1 - simple
sp3.dvi
3 15 5 22 1 2 1.1... 2 1.2... 4 1.3... 5 1.4... 8 1.5 (Matlab )... 11 2 15 2.1... 15 2.2... 16 2.3... 17 3 19 3.1... 19 3.2... 2 3.3... 21 3.4... 22 3.5... 23 3.6... 24 3.7... 25 3.8 Daubechies... 26 4
2.2 (a) = 1, M = 9, p i 1 = p i = p i+1 = 0 (b) = 1, M = 9, p i 1 = 0, p i = 1, p i+1 = 1 1: M 2 M 2 w i [j] w i [j] = 1 j= w i w i = (w i [ ],, w i [
![2.2 (a) = 1, M = 9, p i 1 = p i = p i+1 = 0 (b) = 1, M = 9, p i 1 = 0, p i = 1, p i+1 = 1 1: M 2 M 2 w i [j] w i [j] = 1 j= w i w i = (w i [ ],, w i [](/thumbs/93/111684107.jpg "2.2 (a) = 1, M = 9, p i 1 = p i = p i+1 = 0 (b) = 1, M = 9, p i 1 = 0, p i = 1, p i+1 = 1 1: M 2 M 2 w i [j] w i [j] = 1 j= w i w i = (w i [ ],, w i [")
RI-002 Encoding-oriented video generation algorithm based on control with high temporal resolution Yukihiro BANDOH, Seishi TAKAMURA, Atsushi SHIMIZU 1 1T / CMOS [1] 4K (4096 2160 /) 900 Hz 50Hz,60Hz 240Hz
1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0
A c 2008 by Kuniaki Nakamitsu 1 1.1 t 2 sin t, cos t t ft t t vt t xt t + t xt + t xt + t xt t vt = xt + t xt t t t vt xt + t xt vt = lim t 0 t lim t 0 t 0 vt = dxt ft dft dft ft + t ft = lim t 0 t 1.1
main.dvi
6 FIR FIR FIR FIR 6.1 FIR 6.1.1 H(e jω ) H(e jω )= H(e jω ) e jθ(ω) = H(e jω ) (cos θ(ω)+jsin θ(ω)) (6.1) H(e jω ) θ(ω) θ(ω) = KωT, K > 0 (6.2) 6.1.2 6.1 6.1 FIR 123 6.1 H(e jω 1, ω
Optical Flow t t + δt 1 Motion Field 3 3 1) 2) 3) Lucas-Kanade 4) 1 t (x, y) I(x, y, t)
http://wwwieice-hbkborg/ 2 2 4 2 -- 2 4 2010 9 3 3 4-1 Lucas-Kanade 4-2 Mean Shift 3 4-3 2 c 2013 1/(18) http://wwwieice-hbkborg/ 2 2 4 2 -- 2 -- 4 4--1 2010 9 4--1--1 Optical Flow t t + δt 1 Motion Field
09 8 9 3 Chebyshev 5................................. 5........................................ 5.3............................. 6.4....................................... 8.4...................................
http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
Fourier (a) C, (b) C, (c) f 2 (a), (b) (c) (L 2 ) (a) C x : f(x) = a 0 2 + (a n cos nx + b n sin nx). ( N ) a 0 f(x) = lim N 2 + (a n cos nx + b n sin
( ) 205 6 Fourier f : R C () (2) f(x) = a 0 2 + (a n cos nx + b n sin nx), n= a n = f(x) cos nx dx, b n = π π f(x) sin nx dx a n, b n f Fourier, (3) f Fourier or No. ) 5, Fourier (3) (4) f(x) = c n = n=
. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u(
3 8. (.8.)............................................................................................3.............................................4 Nermark β..........................................
小川／小川
T pt T T T T p T T T T T p T T T T T T p p T T T p p T p B T T T T T pt T Tp T p T T psp T p T p T p T p T p Tp T p T p T T p T T T T T T T Tp T p p p T T T T p T T T T T T T p T T T T T p p T T T T T
Interest Operator Scale Space Wavelet SIFT Interest Operator 2 corner detector 1) SUSAN 3) Harris Shi Tomasi Good feat
2 -- 2 2 2010 5 1 Interest Operator Scale Space Wavelet 1 DP 2-1 Interest Operator 2-1-1 Scale space 2-1-2 Wavelet 2-1-3 SIFT 2-1-4 2-2 2-2-1 DP 2-2-2 2-2-3 c 2012 1/(21) 2 -- 2 -- 2 2--1 2009 9 Interest
Microsoft PowerPoint - 山形大高野send ppt [互換モード]
![Microsoft PowerPoint - 山形大高野send ppt [互換モード]](/thumbs/96/127884904.jpg "Microsoft PowerPoint - 山形大高野send ppt [互換モード]")
, 2012 10 SCOPE, 2012 10 2 CDMA OFDMA OFDM SCOPE, 2012 10 OFDM 0-20 Relative Optical Power [db] -40-60 10 Gbps NRZ BPSK-SSB 36dB -80-20 -10 0 10 20 Relative Frequency [GHz] SSB SSB OFDM SSB SSB OFDM OFDM
it-ken_open.key
深層学習技術の進展 ImageNet Classification 画像認識 音声認識 自然言語処理 機械翻訳 深層学習技術は これらの分野において 特に圧倒的な強みを見せている Figure (Left) Eight ILSVRC-2010 test Deep images and the cited4: from: ``ImageNet Classification with Networks et
dfilterh.dvi
12.5 3 ISBN4-7856-1194-4 C3055 12.5.1 x(t) =A sin(t) rad/sec T s =1=F s t = nt s n x(nt s )=Asin(nT s ) F s! =T s x(nt s )! x(n) x(n) =A sin(nt s )=Asin(!n)! rad { F (Hz) =2F { f! =2f f {! f F! = T s ==F
ウェーブレット分数を用いた金融時系列の長期記憶性の分析
TOPIX E-mail: masakazu.inada@boj.or.jp wavelet TOPIX Baillie Gourieroux and Jasiak Elliott and Hoek TOPIX I (0) I (1) I (0) I (1) TOPIX ADFAugmented Dickey-Fuller testppphillips-perron test I (1) I (0)
impulse_response.dvi
5 Time Time Level Level Frequency Frequency Fig. 5.1: [1] 2004. [2] P. A. Nelson, S. J. Elliott, Active Noise Control, Academic Press, 1992. [3] M. R. Schroeder, Integrated-impulse method measuring sound
untitled
1 SS 2 2 (DS) 3 2.1 DS................................ 3 2.2 DS................................ 4 2.3.................................. 4 2.4 (channel papacity)............................ 6 2.5........................................
Microsoft Word - 信号処理3.doc
Junji OHTSUBO 2012 FFT FFT SN sin cos x v ψ(x,t) = f (x vt) (1.1) t=0 (1.1) ψ(x,t) = A 0 cos{k(x vt) + φ} = A 0 cos(kx ωt + φ) (1.2) A 0 v=ω/k φ ω k 1.3 (1.2) (1.2) (1.2) (1.1) 1.1 c c = a + ib, a = Re[c],
ｽﾗｲﾄﾞ ﾀｲﾄﾙなし
(1) - E-Mail: katto@waseda.jp Y U V R G B (1/30 ) RGB / YUV = B G R V U Y 0.31 0.52 0.21 0.32 0.28 0.60 0.11 0.59 0.30 RGB YUV CCIR 601 4:4:4 4:2:2 4:2:0 Y Y Y U V U V U V YUVUV UV 4:2:0 4:2:2 (RGB8 )
1 1.1 Excel Excel Excel log 1, log 2, log 3,, log 10 e = ln 10 log cm 1mm 1 10 =0.1mm = f(x) f(x) = n
1 1.1 Excel Excel Excel log 1, log, log,, log e.7188188 ln log 1. 5cm 1mm 1 0.1mm 0.1 4 4 1 4.1 fx) fx) n0 f n) 0) x n n! n + 1 R n+1 x) fx) f0) + f 0) 1! x + f 0)! x + + f n) 0) x n + R n+1 x) n! 1 .
09RW-res.pdf
- "+$,&!"'$%"'&&!"($%"(&&!"#$%"#&&!"$%"&& 2009, http://c-faculty.chuo-u.ac.jp/ nishioka/ 2 11 38 : 5 ( 1.1!"*$%"*&& W path, x (i ρ 1, ρ 2, ±1. n, 2 n paths. 1 ρ 1, ρ 2, {1, 1}. a n, { a, n = 0 (1.1 w(n
2012 A, N, Z, Q, R, C
2012 A, N, Z, Q, R, C 1 2009 9 2 2011 2 3 2012 9 1 2 2 5 3 11 4 16 5 22 6 25 7 29 8 32 1 1 1.1 3 1 1 1 1 1 1? 3 3 3 3 3 3 3 1 1, 1 1 + 1 1 1+1 2 2 1 2+1 3 2 N 1.2 N (i) 2 a b a 1 b a < b a b b a a b (ii)
6. Euler x
...............................................................................3......................................... 4.4................................... 5.5......................................
power.tex
Contents ii 1... 1... 1... 7... 7 3 (DFFT).................................... 8 4 (CIFT) DFFT................................ 10 5... 13 6... 16 3... 0 4... 0 5... 0 6... 0 i 1987 SN1987A 0.5 X SN1987A
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
Design of highly accurate formulas for numerical integration in weighted Hardy spaces with the aid of potential theory 1 Ken ichiro Tanaka 1 Ω R m F I = F (t) dt (1.1) Ω m m 1 m = 1 1 Newton-Cotes Gauss
2003/3 Vol. J86 D II No.3 2.3. 4. 5. 6. 2. 1 1 Fig. 1 An exterior view of eye scanner. CCD [7] 640 480 1 CCD PC USB PC 2 334 PC USB RS-232C PC 3 2.1 2
![2003/3 Vol. J86 D II No.3 2.3. 4. 5. 6. 2. 1 1 Fig. 1 An exterior view of eye scanner. CCD [7] 640 480 1 CCD PC USB PC 2 334 PC USB RS-232C PC 3 2.1 2](/thumbs/42/22941906.jpg "2003/3 Vol. J86 D II No.3 2.3. 4. 5. 6. 2. 1 1 Fig. 1 An exterior view of eye scanner. CCD [7] 640 480 1 CCD PC USB PC 2 334 PC USB RS-232C PC 3 2.1 2")
Curved Document Imaging with Eye Scanner Toshiyuki AMANO, Tsutomu ABE, Osamu NISHIKAWA, Tetsuo IYODA, and Yukio SATO 1. Shape From Shading SFS [1] [2] 3 2 Department of Electrical and Computer Engineering,
10
2005 APR no.76 P P P P11P22 P2 P29 P30 P32 / / 787-8501 -10 TEL3-1111 FAX0120-59787 http//www.city.nakamura.kochi.jp/ http://www.city.nakamura.kochi.jp/i/ E-mailkouhou@city.nakamura.kochi.jp 10 10 10 29
2008 : 80725872 1 2 2 3 2.1.......................................... 3 2.2....................................... 3 2.3......................................... 4 2.4 ()..................................
7) ẋt) =iaω expiωt) ibω exp iωt) 9) ẋ0) = iωa b) = 0 0) a = b a = b = A/ xt) = A expiωt) + exp iωt)) = A cosωt) ) ) vt) = Aω sinωt) ) ) 9) ) 9) E = mv
- - m k F = kx ) kxt) =m d xt) dt ) ω = k/m ) ) d dt + ω xt) = 0 3) ) ) d d dt iω dt + iω xt) = 0 4) ω d/dt iω) d/dt + iω) 4) ) d dt iω xt) = 0 5) ) d dt + iω xt) = 0 6) 5) 6) a expiωt) b exp iωt) ) )
特集_03-07.Q3C
3-7 Error Detection and Authentication in Quantum Key Distribution YAMAMURA Akihiro and ISHIZUKA Hirokazu Detecting errors in a raw key and authenticating a private key are crucial for quantum key distribution
2009 IA I 22, 23, 24, 25, 26, a h f(x) x x a h
009 IA I, 3, 4, 5, 6, 7 7 7 4 5 h fx) x x h 4 5 4 5 1 3 1.1........................... 3 1........................... 4 1.3..................................... 6 1.4.............................. 8 1.4.1..............................
4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( )
![4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( )](/thumbs/40/20574692.jpg "4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( )")
RAW 4 E-mail: hakiyama@ok.ctrl.titech.ac.jp Abstract RAW RAW RAW RAW RAW 4 RAW RAW RAW 1 (CFA) CFA Bayer CFA [1] RAW CFA 1 2 [2, 3, 4, 5]. RAW RAW RAW RAW 3 [2, 3, 4, 5] (AWGN) [13, 14] RAW 2 RAW RAW RAW
1 Fourier Fourier Fourier Fourier Fourier Fourier Fourier Fourier Fourier analog digital Fourier Fourier Fourier Fourier Fourier Fourier Green Fourier
Fourier Fourier Fourier etc * 1 Fourier Fourier Fourier (DFT Fourier (FFT Heat Equation, Fourier Series, Fourier Transform, Discrete Fourier Transform, etc Yoshifumi TAKEDA 1 Abstract Suppose that u is
168. W rdrop. W rdrop ( ).. (b) ( ) OD W rdrrop r s x t f c q δ, 3.4 ( ) OD OD OD { δ, = 1 if OD 0
167 p (n) im p(n+1) im p (n+1) im p(n) im < ε (3.264) ε p (n+1) im 1 4 [1],, :, Vol.43, pp.14-21, 2001. [2] Rust, J., Optiml Replcement of GMC Bus Engines: An Empiricl Model of Hrold Zurcher, Econometric,
2 Poisson Image Editing DC DC 2 Poisson Image Editing Agarwala 3 4 Agarwala Poisson Image Editing Poisson Image Editing f(u) u 2 u = (x
1 Poisson Image Editing Poisson Image Editing Stabilization of Poisson Equation for Gradient-Based Image Composing Ryo Kamio Masayuki Tanaka Masatoshi Okutomi Poisson Image Editing is the image composing
13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x
X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n
. 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n
SAMA- SUKU-RU Contents p-adic families of Eisenstein series (modular form) Hecke Eisenstein Eisenstein p T
SAMA- SUKU-RU Contents 1. 1 2. 7.1. p-adic families of Eisenstein series 3 2.1. modular form Hecke 3 2.2. Eisenstein 5 2.3. Eisenstein p 7 3. 7.2. The projection to the ordinary part 9 3.1. The ordinary
23 7 28 i i 1 1 1.1................................... 2 1.2............................... 3 1.2.1.................................... 3 1.2.2............................... 4 1.2.3 SI..............................
CDMA (high-compaciton multicarrier codedivision multiple access: HC/MC-CDMA),., HC/MC-CDMA,., 32.,, 64. HC/MC-CDMA, HC-MCM, i
24 Investigation on HC/MC-CDMA Signals with Non-Uniform Frequency Intervals 1130401 2013 3 1 CDMA (high-compaciton multicarrier codedivision multiple access: HC/MC-CDMA),., HC/MC-CDMA,., 32.,, 64. HC/MC-CDMA,
研究成果報告書
様式 C-19 F-19-1 Z-19 CK-19( 共通 ) 1. 研究開始当初の背景自立走行ロボットの実現には自己位置推定技術が必要であり GPS やレーザーレンジファインダの他にも 映像を用いた高速な処理方法が望まれていた 2. 研究の目的危険個所を自律走行して周囲の状況を映像監視し 通信ネットワークを介して連携できるクローラ型ロボット群が 防災上必要とされている 特にレスキュー現場では 事前の環境情報もなく整備された通信インフラもない
12 DCT A Data-Driven Implementation of Shape Adaptive DCT
12 DCT A Data-Driven Implementation of Shape Adaptive DCT 1010431 2001 2 5 DCT MPEG H261,H263 LSI DDMP [1]DDMP MPEG4 DDMP MPEG4 SA-DCT SA-DCT DCT SA-DCT DDMP SA-DCT MPEG4, DDMP,, SA-DCT,, ο i Abstract
i I II I II II IC IIC I II ii 5 8 5 3 7 8 iii I 3........................... 5......................... 7........................... 4........................ 8.3......................... 33.4...................
N M kb 1 1% 1 kb N M N M N + M ez43-rf2 N M M N/( N) 2 3 WSN Donoho Candès [6], [7] N x x N s x N N Ψ (1) x = Ψs (1) s x s K x
![N M kb 1 1% 1 kb N M N M N + M ez43-rf2 N M M N/( N) 2 3 WSN Donoho Candès [6], [7] N x x N s x N N Ψ (1) x = Ψs (1) s x s K x](/thumbs/88/116097995.jpg "N M kb 1 1% 1 kb N M N M N + M ez43-rf2 N M M N/( N) 2 3 WSN Donoho Candès [6], [7] N x x N s x N N Ψ (1) x = Ψs (1) s x s K x")
Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 1 1,2 1 N M N + M ez43-rf2 N M M N/(1 + 2.82 1 3 N) 1. (WSN) Sink WSN WSN WSN 1 Graduate School of Information Science and Technology, The University of
IPSJ SIG Technical Report 1, Instrument Separation in Reverberant Environments Using Crystal Microphone Arrays Nobutaka ITO, 1, 2 Yu KITANO, 1
1, 2 1 1 1 Instrument Separation in Reverberant Environments Using Crystal Microphone Arrays Nobutaka ITO, 1, 2 Yu KITANO, 1 Nobutaka ONO 1 and Shigeki SAGAYAMA 1 This paper deals with instrument separation
I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
1 P2 P P3P4 P5P8 P9P10 P11 P12
1 P2 P14 2 3 4 5 1 P3P4 P5P8 P9P10 P11 P12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 & 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1! 3 2 3! 4 4 3 5 6 I 7 8 P7 P7I P5 9 P5! 10 4!! 11 5 03-5220-8520
(a) (b) (c) Canny (d) 1 ( x α, y α ) 3 (x α, y α ) (a) A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u ξ α u (A, B, C, D, E, F ) (4) ξ α (x 2 α, 2x α y α,
[II] Optimization Computation for 3-D Understanding of Images [II]: Ellipse Fitting 1. (1) 2. (2) (edge detection) (edge) (zero-crossing) Canny (Canny operator) (3) 1(a) [I] [II] [III] [IV ] E-mail sugaya@iim.ics.tut.ac.jp
数学Ⅱ演習（足助・09夏）
II I 9/4/4 9/4/2 z C z z z z, z 2 z, w C zw z w 3 z, w C z + w z + w 4 t R t C t t t t t z z z 2 z C re z z + z z z, im z 2 2 3 z C e z + z + 2 z2 + 3! z3 + z!, I 4 x R e x cos x + sin x 2 z, w C e z+w
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
2013 M
2013 M0110453 2013 : M0110453 20 1 1 1.1............................ 1 1.2.............................. 4 2 5 2.1................................. 6 2.2................................. 8 2.3.................................
第5章 偏微分方程式の境界値問題
October 5, 2018 1 / 113 4 ( ) 2 / 113 Poisson 5.1 Poisson ( A.7.1) Poisson Poisson 1 (A.6 ) Γ p p N u D Γ D b 5.1.1: = Γ D Γ N 3 / 113 Poisson 5.1.1 d {2, 3} Lipschitz (A.5 ) Γ D Γ N = \ Γ D Γ p Γ N Γ
newmain.dvi
数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published
Fourier Niching Approach for Multi-modal Optimization 2 Yan Pei Hideyuki Takagi 2 Graduate School of Design, Kyushu University 2 2 Faculty of Design,
九州大学学術情報リポジトリ Kyushu University Institutional Repository 多峰性最適化のためのフーリエ ニッチ法 裴, 岩九州大学大学院芸術工学府 高木, 英行九州大学大学院芸術工学研究院 Pei, Yan Graduate School of Design, Kyushu University Takagi, Hideyuki Faculty of Design,
入試の軌跡
4 y O x 7 8 6 Typed by L A TEX ε [ ] 6 4 http://kumamoto.s.xrea.com/plan/.. PDF Ctrl +L Ctrl + Ctrl + Ctrl + Alt + Alt + ESC. http://kumamoto.s.xrea.com/nyusi/qdai kiseki ri.pdf 6 i i..................................
163 KdV KP Lax pair L, B L L L 1/2 W 1 LW = ( / x W t 1, t 2, t 3, ψ t n ψ/ t n = B nψ (KdV B n = L n/2 KP B n = L n KdV KP Lax W Lax τ KP L ψ τ τ Cha
63 KdV KP Lax pair L, B L L L / W LW / x W t, t, t 3, ψ t n / B nψ KdV B n L n/ KP B n L n KdV KP Lax W Lax τ KP L ψ τ τ Chapter 7 An Introduction to the Sato Theory Masayui OIKAWA, Faculty of Engneering,
熊本県数学問題正解
00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (
ii
ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
5 36 5................................................... 36 5................................................... 36 5.3..............................
9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................
Macdonald, ,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdona
Macdonald, 2015.9.1 9.2.,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdonald,, q., Heckman Opdam q,, Macdonald., 1 ,,. Macdonald,
S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
入試の軌跡
4 y O x 4 Typed by L A TEX ε ) ) ) 6 4 ) 4 75 ) http://kumamoto.s.xrea.com/plan/.. PDF) Ctrl +L) Ctrl +) Ctrl + Ctrl + ) ) Alt + ) Alt + ) ESC. http://kumamoto.s.xrea.com/nyusi/kumadai kiseki ri i.pdf
られる DT を とするとき は a 図 π kn [ ]k,n = ejφk,n, φk,n = のように表現され 二次元 DT の atom は Bnk,n,k =, DT の atom B R j φk,n +φk,n e となることから 指向性をもつことがわかる 図 b b DT real
![られる DT を とするとき は a 図 π kn [ ]k,n = ejφk,n, φk,n = のように表現され 二次元 DT の atom は Bnk,n,k =, DT の atom B R j φk,n +φk,n e となることから 指向性をもつことがわかる 図 b b DT real](/thumbs/91/107395480.jpg "られる DT を とするとき は a 図 π kn [ ]k,n = ejφk,n, φk,n = のように表現され 二次元 DT の atom は Bnk,n,k =, DT の atom B R j φk,n +φk,n e となることから 指向性をもつことがわかる 図 b b DT real")
第回信号処理シンポジウム 0年月日 0日 関西大学 双直交指向性離散コサイン変換の設計 Design of Biorthogonal Directional Discrete Cosine Transforms 市田智大 京地清介 鈴木大三 田中雄一 北九州市立大学大学院国際環境工学研究科 筑波大学システム情報系 東京農工大学大学院工学研究院 Tomohiro ICHITA Seisuke KYOCHI
(MIRU2010) Geometric Context Randomized Trees Geometric Context Rand
(MIRU2010) 2010 7 Geometric Context Randomized Trees 487-8501 1200 E-mail: {fukuta,ky}@vision.cs.chubu.ac.jp, hf@cs.chubu.ac.jp Geometric Context Randomized Trees 10 3, Geometric Context, Abstract Image
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
genron-7
F! Z F = * N s/m)! Z R i K # & = " % ) " $ ) ' F R i i K =! " )! +! N) ) R! " i)! i K )! F ) K F = R!, R >> ), R >> ) 3) K F = " i)!, ) >> R, >> ) )! 4) F i K K K =!, > ) ) ) ) F F! 1µ b a r ) V
example2_time.eps
Google (20/08/2 ) ( ) Random Walk & Google Page Rank Agora on Aug. 20 / 67 Introduction ( ) Random Walk & Google Page Rank Agora on Aug. 20 2 / 67 Introduction Google ( ) Random Walk & Google Page Rank
4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q
![4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q](/thumbs/92/110416683.jpg "4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q")
x-means 1 2 2 x-means, x-means k-means Bayesian Information Criterion BIC Watershed x-means Moving Object Extraction Using the Number of Clusters Determined by X-means Clustering Naoki Kubo, 1 Kousuke
HPC pdf
GPU 1 1 2 2 1 1024 3 GPUGraphics Unit1024 3 GPU GPU GPU GPU 1024 3 Tesla S1070-400 1 GPU 2.6 Accelerating Out-of-core Cone Beam Reconstruction Using GPU Yusuke Okitsu, 1 Fumihiko Ino, 1 Taketo Kishi, 2
() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (
3 n nc k+ k + 3 () n C r n C n r nc r C r + C r ( r n ) () n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (4) n C n n C + n C + n C + + n C n (5) k k n C k n C k (6) n C + nc
Duplicate Near Duplicate Intact Partial Copy Original Image Near Partial Copy Near Partial Copy with a background (a) (b) 2 1 [6] SIFT SIFT SIF
![Duplicate Near Duplicate Intact Partial Copy Original Image Near Partial Copy Near Partial Copy with a background (a) (b) 2 1 [6] SIFT SIFT SIF](/thumbs/82/86406952.jpg "Duplicate Near Duplicate Intact Partial Copy Original Image Near Partial Copy Near Partial Copy with a background (a) (b) 2 1 [6] SIFT SIFT SIF")
Partial Copy Detection of Line Drawings from a Large-Scale Database Weihan Sun, Koichi Kise Graduate School of Engineering, Osaka Prefecture University E-mail: sunweihan@m.cs.osakafu-u.ac.jp, kise@cs.osakafu-u.ac.jp
橡Taro11-卒業論文.PDF
Recombination Generation Lifetime 13 9 1. 3. 4.1. 4.. 9 3. Recombination Lifetime 17 3.1. 17 3.. 19 3.3. 4. 1 4.1. Si 1 4.1.1. 1 4.1.. 4.. TEG 3 5. Recombination Lifetime 4 5.1 Si 4 5.. TEG 6 6. Pulse
S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt
S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............
x : = : x x
x : = : x x x :1 = 1: x 1 x : = : x x : = : x x : = : x x ( x ) = x = x x = + x x = + + x x = + + + + x = + + + + +L x x :1 = 1: x 1 x ( x 1) = 1 x 2 x =1 x 2 x 1= 0 1± 1+ 4 x = 2 = 1 ± 5 2 x > 1
5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................
5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)