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main.dvi

5 IIR IIR z 5.1 5.1.1 1. 2. IIR(Infinite Impulse Response) FIR(Finite Impulse Response) 3. 4. 5. 5.1.2 IIR FIR 5.1 5.1 5.2 104 5. IIR 5.1 IIR FIR IIR FIR H(z) = a 0 +a 1 z 1 +a 2 z 2 1+b 1 z 1 +b 2 z 2

main.dvi

2 e jωt, 0 ωt < 2π 2.1 2.1.1 x(n) X(z) = x(n)z n (2.1) z z z = e σ+jωt = re jωt, r = e σ (2.2) ωt 0 2π σ e σ+jωt = re jωt r = e σ 2.1 0

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

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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1 7 ω ω ω 7.1 0, ( ) Q, 7.2 ( Q ) 7.1 ω Z = R +jx Z 1/ Z 7.2 ω 7.2 Abs. admittance (x10-3 S) RLC Series Circuit Y R = 20 Ω L = 100

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2: 3: A, f, φ f(t = A sin(2πft + φ = A sin(ωt + φ ω 2πf 440Hz A ( ( 4 ( 5 f(t = sin(2πf 1t + sin(2πf 2 t = 2 sin(2πt(f 1 + f 2 /2 cos(2πt(f 1 f

12 ( TV TV, CATV, CS CD, DAT, DV, DVD ( 12.1 12.1.1 1 1: T (sec f (Hz T= 1 f P a = N/m 2 1.013 10 5 P a 1 10 5 1.00001 0.99999 2,3 1 2: 3: 12.1.2 A, f, φ f(t = A sin(2πft + φ = A sin(ωt + φ ω 2πf 440Hz

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β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E

[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt

3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

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1. 線形シフト不変システムと z 変換 ここで言う システム とは? 入力数列 T[ ] 出力数列 一意変換 ( 演算子 ) 概念的には,, x 2, x 1, x, x1, x2, を入力すると, y 2, y 1, y, y1, y2, が出力される. 線形システム : 線形システムの例 x nxn 1 yn= 2 線形でないシステムの例 xn yn={ 2 xn xn othewise なぜ線形システム?

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

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2012 A, N, Z, Q, R, C

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Microsoft Word - 信号処理3.doc

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chap1.dvi

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19 Estimation of Sound Source Zone using The Arrival Time Interval 1080351 2008 3 7 S/N 2 2 2 i Abstract Estimation of Sound Source Zone using The Arrival Time Interval Koichiro Kanai The microphone array

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LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University

LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y

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