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 decay without using impulses, J. Acoust. Soc. Am. 66 (2), pp. 497 500, 1979. [4] D. D. Rife, Transfer-function measurement with maximum-length sequences, J. Audio Eng. Soc. 37 (6), pp. 419 444, 1989. [5], ( 4),, 43 (7), pp. 538 543, 1987. [6],,, ( 2),, 45 (1), pp. 44 50, 1989. [7] http://tosa.mri.co.jp/sounddb/tsp/tsp design.html [8],,, 58 (10), pp. 669 676, 2002. [9], Swept-Sine,, 63 (6), pp. 322 327, 2007. [10], SN TSP,, pp. 433-434, 1999,9. 1
5.1 cos(ωt) ω 1Hz 100 Hz t 0.5 +0.5 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
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
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) 5.2.3 Maximum Length Sequence: MLS M (maximum length sequence signal) M 1 L =2 N 1 2 1 1 mls.m M >> xm=mls(5); 4
2 5 1=31 1) M 2) 5.2.4 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
5.3 Swept-Sine Swept-Sine TSP: Time Stretched Pulse Swept-Sine 5.3.1 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 = 1024 1) tsp design Swept-Sine 2) s g 2 7) 6
5.3.2 N L (L = N) I L >I 1. Fig. 5.3 (a) 2. 2000 2 2048 Fig. 5.3 (b) 3. Fig.5.3 (c)) 3 (d) 4 3 4. 4 3 Fig.5.3 (e)) 5. (f) 6. (e) (e) (f) N FFT 7. FFT (g) 7
(a) (b) Swept-Sine 500 1000 1500 2000 500 1000 1500 2000 (c) (d) 2000 4000 6000 8000 2000 4000 6000 8000 (e) (f) 500 1000 1500 2000 500 1000 1500 2000 (g) 200 400 600 800 1000 1200 1400 1600 1800 2000 Fig. 5.3: 8
5.3.3 N I 1. Fig. 5.4 (a) 2. 2000 2 1024 Fig. 5.4 (b) 3. Fig.5.4 (c)) 3 +300 4. N + I 1 5. 3 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
(a) (b) Swept-Sine 500 1000 1500 2000 200 400 600 800 1000 (c) (d) 2000 4000 6000 8000 2000 4000 6000 8000 (e) + α (f) 1000 2000 3000 200 400 600 800 1000 (g) 500 1000 1500 2000 2500 3000 3500 4000 Fig. 5.4: 10
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 5.3.5 p 2 (t) = t h 2 (t) (19) p 2 (t) h(t) t >> p2 = fliplr ( cumsum ( fliplr ( h.^ 2 ) ) ); 11
60 db 1) real ir 48000 Hz 2 ir load 2) fir1 500 Hz 3) fliplr cumsum 4) polyfit 12