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1 5 Time Time Level Level Frequency Frequency Fig. 5.1: [1] [2] P. A. Nelson, S. J. Elliott, Active Noise Control, Academic Press, [3] M. R. Schroeder, Integrated-impulse method measuring sound decay without using impulses, J. Acoust. Soc. Am. 66 (2), pp , [4] D. D. Rife, Transfer-function measurement with maximum-length sequences, J. Audio Eng. Soc. 37 (6), pp , [5], ( 4),, 43 (7), pp , [6],,, ( 2),, 45 (1), pp , [7] design.html [8],,, 58 (10), pp , [9], Swept-Sine,, 63 (6), pp , [10], SN TSP,, pp , 1999,9. 1

2 5.1 cos(ωt) ω 1Hz 100 Hz t cos sum.m 1) 2) t =0 5.2 S/N x(t) y(t) y(t) =h(t) x(t) = h(t) h(t)x(t τ)dτ (1) x(t) h(t) y(t) Fig. 5.2: x(t), h(t), y(t) 2

3 5.2.1 x(t) y(t) 1 T R x (τ) =E[x(t)x(t + τ)] = lim x(t)x(t + τ)dt (2) T T 0 1 T R xy (τ) =E[x(t)y(t + τ)] = lim x(t)y(t + τ)dt (3) T T E[x(t)x(t + τ)] x(t)x(t + τ) R xy (τ) [ R xy (τ) =E x(t) = = 0 h(τ 1 )x(t + τ τ 1 )dτ 1 ] h(τ 1 )E [x(t)x(t + τ τ 1 )dt] dτ 1 h(τ 1 )R x (τ τ 1 )dτ 1 = h(τ) R x (τ) (4) x(t) y(t) R xy (τ) R x (τ) h(τ) R x (τ) =δ(τ) y (t) =y(t)+n(t) R xy (τ) =E[x(t)y (t + τ)] = E[x(t){y(t + τ)+n(t + τ)}] = E[x(t)y(t + τ)] + E[x(t)n(t + τ)] (5) R xy (τ) =E[x(t)y(t + τ)] = R xy (τ) 3

4 5.2.2 R x R xy S x (f) = S xy (f) = R x (τ)e jωτ dτ (6) R xy (τ)e jωτ dτ (7) (8) Eq. (4) S xy (f) =H(f) S x (f) (9) H(f) H(f) = S xy(f) S x (f) (10) S x (f) =E[X (f) X(f)] (11) S xy (f) =E[X (f) Y (f)] (12) x(t) y(t) x(n),y(n) Maximum Length Sequence: MLS M (maximum length sequence signal) M 1 L =2 N mls.m M >> xm=mls(5); 4

5 2 5 1=31 1) M 2) y(t) =h(t) x(t) Y (f) =H(f) X(f) (13) DFT H(f) = Y (f) X(f) (14) 1) impulse data.mat ir, x, y, fs 4 ir 1,000 Hz 2,000 2 x 1 30 y y = fftfilt(ir, x); x, y ir 2) imp fft.m 1 imp fft.m Fig. repo8-1.fig repo8-2.fig subplot(2,1,1) (ir) subplot(2,1,2) 5

6 5.3 Swept-Sine Swept-Sine TSP: Time Stretched Pulse Swept-Sine Swept-Sine Swept-Sine ( j4mπk 2 exp S(k) = N 2 S (N k), ), 0 k N 2 N 2 <k<n (15) m = N/4,N =2 n, n FFT ( j4mπk 2 exp S 1 (k) = N 2 S 1 (N k), ), 0 k N 2 N 2 <k<n (16) tsp design n s g >> [s, g] = tsp design(10); 2 10 = ) tsp design Swept-Sine 2) s g 2 7) 6

7 5.3.2 N L (L = N) I L >I 1. Fig. 5.3 (a) Fig. 5.3 (b) 3. Fig.5.3 (c)) 3 (d) Fig.5.3 (e)) 5. (f) 6. (e) (e) (f) N FFT 7. FFT (g) 7

8 (a) (b) Swept-Sine (c) (d) (e) (f) (g) Fig. 5.3: 8

9 5.3.3 N I 1. Fig. 5.4 (a) Fig. 5.4 (b) 3. Fig.5.4 (c)) N + I Fig.5.4 (e)) 6. (f) 7. (e) conv() fftfilt 8. (g) impulse data mat tsp design Fig. 5.3, 5.4 repo9-1.fig, repo9-2.fig 9

10 (a) (b) Swept-Sine (c) (d) (e) + α (f) (g) Fig. 5.4: 10

11 5.3.4 Swept-Sine Swept-Sine Pink TSP 10) Pink S/N 1 k =0 exp(jak log k) S(k) = k, 0 <k N (17) 2 S N (N k), 2 <k<n a N ( ) N 2 log =2mπ m = N/4,N =2 n, n FFT 2 1 k =0 S 1 N (k) = k exp ( jak log k), 0 k 2 S 1 N (N k), 2 <k<n 1) tsp design Pink-Swept-Sine (18) 2) spectrogram 3) s g p 2 (t) = t h 2 (t) (19) p 2 (t) h(t) t >> p2 = fliplr ( cumsum ( fliplr ( h.^ 2 ) ) ); 11

12 60 db 1) real ir Hz 2 ir load 2) fir1 500 Hz 3) fliplr cumsum 4) polyfit 12

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