Copyright cfl 24 by Yuichi ISHIMOTO
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- かねろう やがい
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1 JAIST Reposi Title 時間情報と周波数情報を用いた雑音環境における基本 周波数推定に関する研究 Author(s) 石本, 祐一 Citation Issue Date 24-3 Type Thesis or Dissertation Text version author URL Rights Description Supervisor: 赤木正人, 情報科学研究科, 博士 Japan Advanced Institute of Science and
2 Copyright cfl 24 by Yuichi ISHIMOTO
3
4 3 ( ) ( ) - 3 (1) - -
5 3dB (2) - (3) -
6 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ( ) : : : : : : : : : : ( ) : : : : : : : : : : ( ) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 i
7 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 82 ii
8 5.2.6 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : A : : : : 94 A.1 : : : : : 94 A.2 YIN : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 96 B : : : 98 B.1 : : 98 B.2 STRAIGHT-TEMPO : : : : : : : : : : : : : : : : : : : : : : iii
9 1 1
10 ( ) 1.2 [1,2] [3, 4] ( ) ( ) [5,6,7] 2
11 1.1: ( [1]) 1.2: 3
12 Amplitude Amplitude Time [ms] Time [ms] 1.3: : ( ) /aoi/ ( ) /aoi/ 12 Amplitude [db] Frequency [Hz] 1.4: /a/ 4
13 [8, 9, 1] [11] Bregman [12] [13,14] 1.2 [15, 16, 17] Hz Hz
14 1.5 2 [18] 2 2 ( ) 1/2 ( ) 3. Electroglottograph(EGG) 3 6
15 5 [Hz] [Hz] 1.5: ( [18]) 1.3 [19, 2, 21] 1. ( ) 2. ( ) 1.4 7
16 1.6: (Gold and Rabiner[22]) Gold and Rabiner [22] Geοckinli and Yavuz [23] 8
17 Autocorrelation functions Pooled autocorrelation function 1.7: (Meddis[35]) [24] (AMDF) [25] [26] AMDF [27] (YIN)[28] LPC [29] LPC Markel LPC (SIFT) [3] LPC 1.7 [31] 9
18 1.1: ( ) [22] [36] [23] [37] [24] [38] [39] [4] [41] [42] [43] [44] [26] AMDF [27] LPC [29] SIFT [3] [31] [35] [32] [33] (AMDF) [25] [45] [46] (YIN) [28] [34] [47] [48] [32,33,34] [49] [5] comb filter comb filter comb filtering [51] [52] - Unoki and Akagi comb filtering [14] Unoki 1
19 4 ms [53,54] [55] [56,57] [7] [58, 59, 6, 61] Kawahara (STRAIGHT-TEMPO) [62] [63] [64] STRAIGHT-TEMPO ffl (AC)[26] 11
20 1.2: ( ) [65] [5] [66] [67] [14] [68] [51] [69] [7] [71] [72] [73] (SHS) [52] [74] [75] [53][54] [56] [57] [55] [7] [58] [59] [76] [6] [61] [77] STRAIGHT-TEMPO [62] [63] [64] ffl (YIN)[28] YIN ffl (CEP)[55] ffl (STRAIGHT-TEMPO)[62] STRAIGHT-TEMPO 12
21 4 ( ) - 4 Electroglottograph(EGG) EGG 2 EGG EGG 1 2 EGG - 1 EGG 13
22 Speech wave 1 Amplitude EGG 1 Amplitude Time [ms] 1.8: : ( ) ( )EGG EGG [63] 14 3 ( 84 ) EGG 1.8 EGG 16 khz - / e(n) e(n) =F (n) F e (n) (1.1) F (n) F e (n) 1 N v X μe = 1 N v N v 2 2 n je(n)j (1.2) Gross error : N v je(n)j :2 F (n) N e Gross error = N e N v 1 [%] (1.3) 14
23 1.3: EGG [Hz] AC YIN CEP TEMPO AC YIN CEP TEMPO ±2% Fine error : je(n)j < :2 F (n) N c Fine error = 1 XN c je(n)j 1 [%] (1.4) N c F (n) ±2% Gross error Fine error 2 EGG (Hz) (%) ( 1) EGG 1.3 STRAIGHT-TEMPO 2.8 Hz 2.9 Hz YIN 4.5 Hz STRAIGHT-TEMPO 4.9 Hz 6.1 Hz 4 STRAIGHT-TEMPO - ( 2) n 15
24 15 1 Gross error [%] 5 AC YIN CEP STRAIGHT -TEMPO 1.9: Gross error Fine error [%] AC YIN CEP STRAIGHT -TEMPO 1.1: Fine error 16
25 EGG Gross error 1.9 EGG STRAIGHT- TEMPO Fine error 1.1 ±2% STRAIGHT-TEMPO 4 STRAIGHT-TEMPO - 1 STRAIGHT- TEMPO STRAIGHT-TEMPO 2 EGG STRAIGHT-TEMPO STRAIGHT-TEMPO EGG STRAIGHT-TEMPO 2 : : 1 3dB 2 (Signal to Noise Ratio; SNR) 1 db Gross error Fine error 17
26 EGG STRAIGHT-TEMPO Gross error Fine error - Gross error 1.11 File error 1.12 STRAIGHT-TEMPO Gross error Gross error Gross error Fine error STRAIGHT-TEMPO ±2% Fine error - Gross error 1.13 File error 1.14 STRAIGHT-TEMPO 1. 18
27 AC YIN CEP STRAIGHT -TEMPO 35 Gross error [%] SNR [db] : Gross error AC YIN CEP STRAIGHT-TEMPO 3.5 Fine error [%] SNR [db] : Fine error 19
28 6 5 AC YIN CEP STRAIGHT-TEMPO 4 Gross error [%] SNR [db] : Gross error AC YIN CEP STRAIGHT-TEMPO 3.5 Fine error [%] SNR [db] : Fine error 2
29 (STRAIGHT-TEMPO) 2. (, ) 1.4 ( )
30 1.15: ( [78]) [79] 1.16 [3, 33] 2 22
31 1.16: ( [4]) 23
32 ( phase locking ) 5 khz [33,8]
33 1 Amplitude Frequency [Hz] Time [ms] 1.17: [81] 1 Amplitude Frequency [Hz] Time [ms] 1.18: [82] 25
34 ( ) ( )
35 1.4 ( )
36 [83, 84, 85] 28
37 ( )
38 [16, 17] 1.2 ffl ffl 1.6 3
39 ( ) ( ) /
40 4 3 ( ) ( )
41 1.19: 33
42 2 34
43 ffl ffl
44 ( ) Unoki and Akagi comb filtering [14] Q - - Unoki 36
45 Amplitude 1-1 Amplitude Time [ms] 3 F [Hz] Time [ms] 1 Amplitude Time [ms] 4 Frequency [Hz] Correlation coefficient Time [ms] 1 Amplitude Time [ms] 4 3 F [Hz] Time [ms] 2.1: 37
46 - Unoki ( ) ( ) - Q 2 - Q ( ) ( ) ( ) 2 Dempster 38
47 ( ) 39
48 ( ) (STRAIGHT-TEMPO)[62] STRAIGHT-TEMPO
49 3 4 41
50 3 42
51 Q 2 - Q 43
52 time [ms] frequency [Hz] time [ms] τ [ms] frequency [Hz] time [ms] ζ [Hz] τ [ms] ζ [Hz] τ [ms] : 44
53 ( ) 2 Dempster [86,87] Dempster x(t) h k (t) y k (t) y k (t) =x(t) Λ h k (t); (3.1) k Λ ~y k (t) ~y k (t) = F 1 [2Y k (!)U(!)] ; (3.2) U(!) = 8 >< >: 1;!> 1=2;! = ;!< (3.3) Y k (!) y k (t) F 1 [ ] s k (t) k (t) (3.4) (3.5) s k (t) = j~y k (t)j; (3.4) 45
54 Amplitude Frequency [Hz] 3.2: Q k arg ~y k(t): (3.5) - Q 2 (3.6) [88] gt(t) =At N 1 exp( 2ßb f ERB(f c )t)cos(2ßf c t); (t >) (3.6) N b f f c ERB(f c ) Equivalent Rectangular Bandwidth[89] Q [9] h k (t) = p 1 t gt ; (3.7) a a a = 1 (2=K)(k 1) 1 ; (3.8) 46
55 Amplitude Frequency [Hz] 3.3: ( 1, 1,2,...,4 ) N =4;f c =6Hz,b f =1; 1» k» K +1;K=64 (3.1) 6 6 Hz 33 Q 3.2 h k (t) h k (t) = At N 1 exp( 2ßb f t)cos(2ßf k t); (t >) (3.9) f k = 6 + 5(k 1) Hz; (3.1) N =4;b f = 2 Hz,1» k» Hz 4 2 khz 2 khz
56 s k (t) Q - Q (FFT) (3.9) FFT 3.4 Q /a/( 3.4 ) ms t k fi a k;t (fi) a k;t (fi) = t+w X t i=t μs k (i)μs k (i + fi); (3.11) μs k (t) = C[s k (t)] (3.12) 48
57 2 Amplitude Channel # Amplitude Time [ms] 3.4: - /a/ : ( ) /a/ ( ) Q - ( ) 49
58 2 Amplitude Channel # Time [ms] Amplitude Channel # 3.5: - /a/ : ( ) /a/ ( ) - ( ) 8 ms 5
59 Cx [ ] C L C L x 3.6: w t 35 ms μs k (t) s k (t) [24] C[ ] 3.6 ( ) a t (fi) = 1 N X p N p k=1 a k;t (fi) (3.13) N p Q (N p = 33) Q Meddis [31] Gold and Rabiner [22] - t f b f;t ( ) Xw e b f;t ( ) = ~s j (t)~s j+ (t) (3.14) j=w f w f ;w e 51
60 ( ) b t;f ( ) X b t ( ) = 1 N h b f;t ( ) (3.15) N h N h a t (fi);b t ( ) ( ) fi a t (fi) - b t ( ) a t (fi) - b t ( ) fi f t a t (fi) b t ( ) b t ( ) ~ b t (fi) a t (fi) ~ b t (fi) a t (fi) ~ b t (fi) a t (fi).9 ~ b t (fi).9 a t (fi) =1:; ~ b t (fi) =:1 fi Bayes a t (fi) ~ b t (fi) =1: :1 = :1 a t (fi) =1: fi a t (fi) ~ b t (fi) a t (fi) ~ b t (fi) a t (fi)=.9 fi.9 1: a t (fi) =:1 fi fi 52
61 Amplitude F [Hz] τ ζ time [ms] 3.7: a t (fi);b t ( ): ( a t (fi) - b t ( ) - ) 53
62 Amplitude F [Hz] τ ζ time [ms] 3.8: a t (fi);b t ( ): ( a t (fi) - b t ( ) - ) 54
63 a t (fi) ~ b t (fi) Bayes Dempster & Shafer [86] Dempster & Shafer Bayes (p(a)+p( A)=1) μ a t (fi) m 1 (A fi )(A fi fi ) 1 a t (fi) ( ) m 1 (A fi ; Afi μ ) m 2 (A fi )= ~ b t (fi); m 2 (A fi ; A μ fi )=1 ~ b t (fi) Dempster X m 1 (A 1i )m 2 (A 2j ) A 1i A 2j =A k m(a k )= X 1 m 1 (A 1i )m 2 (A 2j ) A 1i A 2j =ffi (3.16) c t (fi) = a t (fi) ~ b t (fi)+(1 a t (fi)) ~ b t (fi)+a t (fi)(1 ~ b t (fi)) = 1 (1 a t (fi))(1 ~ b t (fi)) (3.17) [87, 91] c t (fi) t ( ) 3.6 ffl ffl 55
64 (3.17) EGG [63] 14 5 ( 14 ) 16 khz : 1 khz : 1kHz 2 SNR 1 db / Gross error : ±2% Gross error EGG STRAIGHT-TEMPO[62] (3.17) c t (fi) (3.13) a t (fi) (3.15) b t ( ) Gross error 3.9 Gross error
65 7 6 Proposed (both) Proposed (periodicity only) Proposed (harmonicity only) 5 Gross error [%] SNR [db] 5 3.9: Gross error 35 3 Proposed (both) Proposed (periodicity only) Proposed (harmonicity only) 25 Gross error [%] SNR [db] 5 3.1: 1 khz Gross error 57
66 a t (fi) Gross error b t ( ) SNR Gross error 1 khz Gross error Gross error (AC)[26] (CEP)[55] Gross error 3.11 Gross error 3.12 SNR 1 db SNR 5 db Gross error Gross error 58
67 25 2 Proposed (both) AC CEP Gross error [%] SNR [db] : 7 6 Proposed (both) AC CEP : 1 khz 59
68 3.13: (3.17) ( )
69 4 x Correlation coeffcient 3.14: : ±2% ( ) ±2% ( ) 4 x Correlation coeffcient 3.15: 1 khz : ±2% ( ) ±2% ( ) 61
70 ±2% ±2% 3.14( ) ±2% 3.14( ) ±2% 3.15( ) ±2% 3.15( ) 3.14( ) ( ) ( ) ( ) ±2%.5 ±2% Dempster 62
71
72 4 64
73 4.1 3 ffl ffl s(t) n(t) x(t) x(t) = s(t)+n(t) = X l a l e j(l! (t)t+ l) + X m b m e j(!mt+ m) (4.1)! (t) = 2ß=T (t) (4.2) T (t) s(t) T (t) T =2ß=! (4.3) 65
74 x(t) 2D + - ˆ s (t) D -D FFT IFFT D=T Fundamental period -2D 4.1: (4.1) x(t) ±T ±2T c(t) = 1 8 f4x(t) x(t T ) x(t + T ) x(t 2T ) x(t +2T )g (4.4) = X m b m e j(!mt+ m) d(! m ) (4.5) d(! m )= cos 2! m ß + cos 4! m ß!! (4.6) c(t) C(! m ) n(t) N(! m ) (4.5) C(! m )=N(! m ) d(! m ) (4.7) C(! m ) N(! m ) d(! m ) N(! m ) N(! m )=C(! m )=d(! m ) (4.8) N(! m ) s(t) =x(t) n(t) (4.9) 1=T! m =! (4.6) d(! m ) = 66
75 (4.8) N(! m ) ^N(! m )= 8 >< >: C(! m )=d(! m ); d(! m ) " C(! m ); d(! m ) <" (4.1) ^n(t) ^s(t) =x(t) ^n(t) (4.11) ^s(t) (4.1) " 4.2 " " 4.3 SNR SNR
76 ε=.1 ε=.3 Gain [db] Gain [db] ε= Frequency [Hz] ε= Frequency [Hz] 4.2: 68
77 EGG [63] 7 5 EGG STRAIGHT-TEMPO[62] SNR 1dB (" = :1 1:.1 ) F (n) Hz ffl F (n)±5 Hz ffl F (n)±5 Hz F (n)±5 Hz F (n)±5 Hz (STRAIGHT-TEMPO) ±2% Gross error 4.3 F (n)± 5Hz ".1 ".3.4 Gross error 4.4 F (n)± 5 Hz 69
78 Gross error [%] Gross error [%] Gross error [%] Gross error [%] Gross error [%] Clean SNR 1 db SNR 5 db SNR 3 db SNR db ε 4.3: " ( F (n)±5 Hz ) " Gross error ".7 Gross error ".8 1. Gross error 5Hz 5 Hz Gross error " " ffl "=.3.4 7
79 Gross error [%] Gross error [%] Gross error [%] Gross error [%] Gross error [%] 1 5 Clean SNR 1 db SNR 5 db SNR 3 db SNR db ε 4.4: " ( F (n)±5 Hz ) ffl "= ffl.5 ± 2% ( ) ffl.5 ± 2% ( ) 71
80 4.3.1 ffl "=.3.4 ffl "=.8 1. ".3.4 Gross error.8 1. ffl.5 " =:3 ffl.5 " =: (4.3) (4.3) T (t) et s (t) = T T (t) T s (4.12) T T (t) T s e T s (t) T s 4.5 (4.12) 72
81 Amplitude Amplitude F [Hz] Time [ms] F [Hz] Time [ms] 4.5: : ( ) ( ) " " kHz SNR 1 db ±2% Gross error " ( ) 4.6( ) 73
82 Gross error [%] Gross error [%] ε: variable ε=.3 ε=.8 ε: variable ε=.3 ε=.8 White noise Band noise (< 1 khz) SNR [db] 4.6: " : ( ) ( ) ".3.8 " =:8 " =:3 Gross error " " =:8 " Gross error " " 74
83
84 5 76
85 5.1 ( ) ( ) EGG [63] 14 3 ( 84 ) EGG 16 khz 4 : : 1 3dB : 77
86 : [81] 48 khz 16 khz SNR 1 db Gross error : ±2% Fine error : ±2% Gross error Fine error ( ) ffl (AC)[26] ffl (YIN)[28] ffl (CEP)[55] ffl (STRAIGHT-TEMPO)[62] 4 78
87 5.2.2 Gross error 5.1 Fine error Gross error SNR 5dB Gross error STRAIGHT-TEMPO Gross error Gross error 5.2 STRAIGHT-TEMPO SNR Fine error Fine error Fine error ±2% Gross error 5.3 Fine error 5.4 SNR 5.3 Gross error Gross error SNR 1 db Gross error SNR 3 db Gross error 79
88 Proposed AC YIN CEP STRAIGHT-TEMPO Gross error [%] SNR [db] 5 5.1: Gross error Proposed AC YIN CEP STRAIGHT-TEMPO Fine error [%] SNR [db] 5 5.2: Fine error 8
89 6 5 Proposed AC YIN CEP STRAIGHT -TEMPO 4 Gross error [%] SNR [db] 5 5.3: Gross error Proposed AC YIN CEP STRAIGHT-TEMPO Fine error [%] SNR [db] 5 5.4: Fine error 81
90 5.4 fine error Gross error 5.5 Fine error YIN STRAIGHT- TEMPO - STRAIGHT-TEMPO Gross error SNR 1 db Gross error 5.6 Fine error STRAIGHT-TEMPO Gross error 5.7 Fine error Gross error SNR - 82
91 9 8 7 Proposed AC YIN CEP STRAIGHT-TEMPO 6 Gross error [%] SNR [db] 5 5.5: Gross error Proposed AC YIN CEP STRAIGHT-TEMPO Fine error [%] SNR [db] 5 5.6: Fine error 83
92 6 5 Proposed AC YIN CEP STRAIGHT -TEMPO 4 Gross error [%] SNR [db] 5 5.7: Gross error Proposed AC YIN CEP STRAIGHT-TEMPO Fine error [%] SNR [db] 5 5.8: Fine error 84
93 5.8 Fine error Fine error Gross error STRAIGHT-TEMPO Gross error STRAIGHT-TEMPO Fine error Fine error Fine error SNR 5 db Gross error ( ) STRAIGHT-TEMPO Gross error Gross error Fine error Gross error 85
94 5.1: Gross error YIN TEMPO SNR db Gross error: ( 2%), (2 3%), (3 4%), (4% ) Fine error YIN TEMPO (SNR db) Fine error : (.5 pt.), (.5 1. pt.), ( pt.), (1.5 pt. ) 86
95 Gross error - SNR Fine error Gross error - Gross error Fine error Fine error 87
96 5.3-88
97 6 89
98 6.1 ffl - ( ) ffl ( ) ffl ( ) 1 9
99
100 A B
101 3. ( ) khz 3 Hz - 93
102 A A [26] A.1 94
103 U n A.1: ( [26] ) N w ( )T n (ms) T n =15:+(n 1)f41:=(N w 1) + :5g; (1» n» N w ) (1) x n 1 n (1) R n (k) R n (k) = L n k 1 X i= x n (i)x n (i + k)=(l n k) (2) L n k min (n)» k» k max (n) R n (k) k k n k min (n), k max (n) 2 k min (n) =:15 L n (n 1)=(N w 1) (3) k n V n k max (n) =L n =2 (4) V n = R n (k n )=R n () (5) 1 Nw =1 T 1 =35: ms Nw =2 T 1 =25: ms,t 2 =45: ms Nw =3 T 1 =21: ms, T 2 =36: ms,t 3 =51: ms Nw 4 Tn 15 ms 2 kmin(n) Nw = ms Nw > ms kmax(n) n = Nw 28.6ms 95
104 Difference function d Cumulative mean normalized difference function d' Parabolic interpolation Search for a minimum of d' Best local estimate A.2: YIN k n U n U n = V n + g nj = 8 >< >: XN w j=1 g nj V j (6) 1; (r nj» :1) (:25 r nj )=:15; (:1 <r nj» :25) ; (:25 <r nj ) r nj = jk j =k n 1j (8) U n n n max k nmax N w (7) A.2 YIN de Cheveigné and Kawahara (YIN) [28] [34, 92] A.2 x(t) T T x(t) x(t + T )= (9) (difference function) d t (fi) = WX j=1 fx(j) x(j + fi)g 2 (1) d t (fi) 96
105 A.3: Cumulative mean normalized difference function (de Cheveigné, Kawahara[28]) fi (1) T d t (T )= fi d t () (cumulative mean normalized difference function) d t(fi) d t (fi) = 8 >< >: 1; fi = d t (fi)= 2 fix 4 (1=fi) j=1 3 (11) d t (j) 5 ; otherwise A.3 d t(fi) d t(fi) d t(fi) [t T max =2;t+ T max =2] d t(fi) T max 97
106 B B.1 LPC Noll [54] x(t) g(t) h(t) x(t) = Z t g(t fi)h(fi)dfi (12) X(!) = G(!)H(!) (13) X(!);G(!);H(!) x(t);g(t);h(t) log jx(!)j =logjg(!)j +logjh(!)j (14) c(fi) c(fi) =F 1 [log jx(!)j] =F 1 [log jg(!)j]+f 1 [log jh(!)j] (15) F 1 (15) 1 98
107 log X(ω) 2 1 T Frequency (Hz) F [ 1 log X(ω) 2 ] Quefrency (seconds) T B.1: : ( ) ( ) (Noll[54]) B.1 Noll [55] B.2 Noll log jx(!)j 99
108 x(t) log X(ω) B.2: (, [55]) B.2 STRAIGHT-TEMPO Kawahara STRAIGHT (STRAIGHT-TEMPO) [62] B.3 x(t)!(t) H[x(t)]!(t) = dffi(t) (16) dt ffi(t) = arg[x(t)+jh[x(t)]] (17) ffi(t) c Gabor w(t; c ) 2 2 h(t; c ) 1
109 B.3: STRAIGHT-TEMPO (Kawahara [62]) a b c F frequency B.4: w s (t; c ) x(t) wavelet h(t; c ) = max Λ w s (t; c ) = w(t; c ) Λ h(t; c ) (18) w(t; c ) = e 2 c t2 4ß 2 e j ct (19) ( fi fi fi ; 1 fi fi ct 2ß B.4!(t; ) ( ) ( ) c B.5 11 fi fi) fi fi fi (2)
110 F F B.5: (Kawahara [62]) C/N (carrier to noise ratio) C/N C/N o ~ff 2 (t) ~ff 2 (t) = c a c a = c b = Z 1 1 Z 1 1 ψ ψ! 2 + c b 2!(t; ) 1 dg( ) o d 1 2 o dg( ) fi fi! 2 fi fi d fi o = o fi fi! 2 fi fi d fi o = o! 2 (21) (22) (23) μff C/N=1=μff 12
111 μff 2 (t; ) = Z Tw T w jw(fi; )j~ff 2 (t fi; )dfi (24) T w jw(fi; )j 13
112 NTT NTT (CREST) 14
113 [1],,,,,,", 199. [2],,,",1981. [3],,, 198. [4],,,,,",199. [5] H. Singer, S. Sagayama, Pitch dependent phone modeling for HMM based speech recognition," Proc. ICASSP92, vol.1,pp ,1992. [6],,, F," 1, pp ,1998. [7],,,,", SP22-13,22. [8] H. Dudley, Remaking speech," J. Acoust. Soc. Amer,vol. 11,pp , [9] M. R. Schroeder, Vocoders: Analysis and synthesis of speech," Proc. of IEEE, vol. 54,no. 5,pp ,1966. [1],,", vol. 37, no. 5, pp ,
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123 1.,,,", SP99-169,2. 2.,,," 12,pp ,2. 3.,,,," 12, p.452,2. 4.,,,," 12, pp ,2. 5.,,,,",H-2-81,2. 6.,,,,",pp ,21. 7.,,,," 13, pp ,21. 8.,,,," 13, pp ,21. 9.,,,,,", SP22-52,22. 1.,,,, F," 14, pp , ,, 115
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JAIST Reposi https://dspace.j Title 質問の曖昧性を考慮した質問応答システムに関する研 究 Author(s) 松本, 匡史 Citation Issue Date 2006-03 Type Thesis or Dissertation Text version author URL http://hdl.handle.net/10119/1986 Rights Description
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