LMS NLMS LMS Least Mean Square LMS Normalized LMS NLMS AD 3 1 h(n) y(n) d(n) FIR w(n) n = 0, 1,, N 1 N N =
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1 LMS NLMS RLS FIR IIR c /(13)
2 LMS NLMS LMS Least Mean Square LMS Normalized LMS NLMS AD 3 1 h(n) y(n) d(n) FIR w(n) n = 0, 1,, N 1 N N = LMS y(n) x(n) h(n) J c /(13)
3 J = E[e 2 (n)] (3 1) = E[{d(n) y(n)} 2 ] = E[d 2 (n) 2d(n)h T x(n) + {h T x(n)}{x T (n)h}] = E[d 2 (n)] 2h T E[d(n)x(n)] + h T E[x(n)x T (n)]h = R dd (0) 2h T P dx + h T R xx h E h = [h 0 h 1...h N 1 ] T x = [x(n)x(n 1)...x(n N + 1)] T R dd (0) d(n) P dx R xx e(n) J E J h (3 1) h Wiener h = R 1 xx P dx (3 2) 2 LMS Wiener 1 2 h(n) Wiener J min Steepest decent LMS for n ++ (3 3) y(n) = h(n)tx(n) e(n) = y(n) d(n) h(n + 1) = h(n) + µe(n)x(n) end h(n + 1) n + 1 µ LMS 2N 3 LMS LMS Wiener (3 3) c /(13)
![..x(n N + 1)] T R dd (0) d(n) P dx R xx e(n) J E J h (3 1) h Wiener h = R 1 xx P dx (3 2) 2 LMS Wiener 1 2 h(n) Wiener J min](/docs-images/56/20090586/images/page_3.jpg "Steepest decent LMS for n ++ (3 3) y(n) = h(n)tx(n) e(n) = y(n) d(n) h(n + 1) = h(n) + µe(n)x(n) end h(n + 1) n + 1 µ LMS 2N 3")
4 E[e(n)x(n)] = E[{d(n) y(n)}x(n)] (3 4) = E[{d(n) x T (n)h}x(n)] = P dx R xx h LMS (3 2) Wiener 1 Wiener NLMS 1 LMS 1) LMS µ 0 < µ < 2 λ max (3 5) λ max x(n) R xx µ R xx R xx R xx tr[r xx ] = M λ k k=1 (3 6) λ k 0 λ max M λ k k=1 (3 7) x(n) σ 2 x tr[r] = E[x 2 (n)] + E[x 2 (n 1)] + + E[x 2 (n N + 1)] = Nσ 2 x (3 8) (3 5) 0 < µ < 2 Nσ 2 x (3 9) µ (3 5) x(n) 2 NLMS (3 5) LMS h(n + 1) = h(n) + αe(n)x(n)/nσ 2 x (3 10) c /(13)
![6) λ k 0 λ max M λ k k=1 (3 7) x(n) σ 2 x tr[r] = E[x 2 (n)] + E[x 2 (n 1)] + + E[x 2 (n N + 1)] = Nσ 2 x (3](/docs-images/56/20090586/images/page_4.jpg "8) (3 5) 0 < µ < 2 Nσ 2 x (3 9) µ (3 5) x(n) 2 NLMS (3 5) LMS h(n + 1) = h(n) + αe(n)x(n)/nσ 2 x (3 10) c")
5 0 < α < 2 LMS NLMS LMS 1) S. Haykin,,,, c /(13)
6 recursive least-squares algorithm RLS 3-1 LMS RLS RLS J(n) n J(n) = λ n i {d(i) w T (n)x(i)} 2 i=1 (3 11) d(i) x(i) w(n) x(i) w(n) x T (i) = [ x(i), x(i 1),..., x(i N + 1) ] (3 12) w T (n) = [ w 0 (n), w 1 (n),..., w N 1 (n) ] (3 13) λ 1 1 (3 11) J(n) ŵ(n) (3 14) R(n)ŵ(n) = θ(n) (3 14) n R(n) = λ n i x(i)x T (i) i=1 (3 15) n θ(n) = λ n i x(i)d(i) i=1 (3 16) (3 15) (3 16) (3 14) ŵ(n) RLS 1) [ RLS ] P(0) = δ 1 I, ŵ(0) = O (3 17) n = 1, 2,... g(n) = P(n 1)x(n) λ + x T (n)p(n 1)x(n) (3 18) c /(13)
![.., w N 1 (n) ] (3 13) λ 1 1 (3 11) J(n) ŵ(n) (3 14) R(n)ŵ(n) = θ(n) (3 14) n R(n) = λ n i x(i)x T (i) i=1 (3 15) n θ(n) = λ n i](/docs-images/56/20090586/images/page_6.jpg "x(i)d(i) i=1 (3 16) (3 15) (3 16) (3 14) ŵ(n) RLS 1) [ RLS ] P(0) = δ 1 I, ŵ(0) = O (3 17) n = 1, 2,.")
7 ν(n) = d(n) ŵ T (n 1)x(n) (3 19) ŵ(n) = ŵ(n 1) + g(n)ν(n) (3 20) P(n) = λ 1 {P(n 1) g(n)x T (n)p(n 1)} (3 21) δ P(n) (3 22) P 1 (n) = R(n) + δλ n I (3 22) RLS (3 11) (3 23) 1) n J(n) = δλ n w(n) λ n i {d(i) w T (n)x(i)} 2 i=1 (3 23) RLS RLS N O(N 2 ) O(N) 1) 2) R(n) RLS 3) RLS 4) R(n) leaky RLS 1) A.H. Sayed and T. Kailath, A state-space approach to adaptive RLS filtering, IEEE Signal Process. Mag., vol.11, no.3, pp.18-60, ) J. Benesty and T. Gänsler, New insights into the RLS algorithm, EURASIP J. Appl. Signal Processing, vol.2004, issue 3, pp ) S.H. Leung and C.F. So, Gradient-based variable forgetting factor RLS algorithm in time-varying environments, IEEE Trans. Signal Processing, vol.53, no.8, pp , ) E. Horita, K. Sumiya, H. Urakami, and S. Mitsuishi, A leaky RLS algorithm: its optimality and implementation, IEEE Trans. Signal Processing, vol.52, no.10, pp , c /(13)
8 FIR 3 2 1) x(i) 3 2 DFT X k (i)(k = 0, 1,, N 1) i k N DFT X k (i) W k (i) IDFT y(i) DFT IDFT FFT FFT (N) 1/N 2) DFT FFT W k (b) = W k (b 1) 1 X k (b) 2 E k(b) X k (b) (3 24) b D k (b) E k (b) D k (b) W k (b)x k (b) c /(13)
9 N N 3 3 3) N x(i n) (n = 0, 1,..., N 1) 3 3 DFT DFT FFT X k (i) W k (i) IDFT d(i) IDFT DFT FFT 1 W k (i) = W k (i 1) 1 X k (i) 2 e(i)x k(i) (3 25) e(i) c /(13)
10 DFT DCT 1) M. Dentino, J. McCool, and B. Widrow, Adaptive Filtering in the Frequency Domain, Proc. of the IEEE, vol.67, no.12, pp , ),,, pp , 3) S.S. Narayan, A.M. Peterson, and M.J. Narasimha, Transform Domain LMS Algorithm, IEEE Trans. Acoustics, Speech, and Signal Processing, vol.31, no.3, pp , ) S. Haykin, Adaptive Filter Theory, pp.18-67, Prentice-Hall, Inc., ) W.K. Jenkins, A.W. Hull, J.C. Strait, B.A. Schnaufer, and X. Li, Advanced Concepts in Adaptive Signal Processing, pp , c /(13)
11 , 2, 3) 2 4, 5) K(z) 3 4 H(z) d(i) s(i) x(i) e(i) c /(13)
12 x(i) K(z) 3 6 d(i) x(i) H(z) C(z) y(i) e(i) = d(i) + y(i) C(z) C(z) K(z)/C(z) 2) LMS C(z) Filtered-X 1) B. Widrow and S.D. Stearns, Adaptive Signal Processing, pp , Prentice-Hall, Inc., c /(13)
13 2),, pp ,, ) S. Haykin, Adaptive Filter Theory, pp.18-67, Prentice-Hall, Inc., ) W.K. Jenkins, A.W. Hull, J.C. Strait, B.A. Schnaufer, and X. Li, Advanced Concepts in Adaptive Signal Processing, pp , ),, 2, pp , c /(13)
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)]
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
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LMS FPGA 18 2 28 0244031 MMSE( Minimum Mean Square Error) MMSE LMS( Least Mean Square), RLS( Recursive Least Mean) ( ) LMS, N-LMS( Normalized - LMS) FPGA( Field Programmable Gate Array) FPGA, 2 FPGA N-LMS
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)
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
3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α
![3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α](/thumbs/42/22937190.jpg "3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α")
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A Study of Adaptive Array Implimentation for mobile comunication in cellular system GD133
A Study of Adaptive Array Implimentation for mobile comunication in cellular system 15 1 31 01GD133 LSI DSP CMA 10km/s i 1 1 2 LS-CMA 5 2.1 CMA... 5 2.1.1... 5 2.1.2... 7 2.1.3... 10 2.2 LS-CMA... 13 2.2.1...
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Kalman ( ) 1) (Kalman filter) ( ) t y 0,, y t x ˆx 3) 10) t x Y [y 0,, y ] ) x ( > ) ˆx (prediction) ) x ( ) ˆx (filtering) )
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SL-8号電話機 取扱説明書
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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
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
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7 2 2.1 A µ : A A A µ(x, y) x y (x y) z = x (y z) A x, y, z x y = y x A x, y A e x e = e x = x A x e A e x A xy = yx = e y x x x y y = x 1 2.1.1 A (1) A = R x y = xy + x + y (2) A = N x y = x y (3) A =
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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
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m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります
Netcommunity SYSTEM αNXⅡ typeS/typeM 取扱説明書
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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
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