IPSJ SIG Technical Report Vol.2012-MUS-94 No.27 Vol.2012-SLP-90 No /2/4 1 2 J K L 3 ( ) GUI Musical Audio Signal Modeling for Joint Estimation

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1 2 J K L 3 GUI Musical Audio Signal Modeling or Joint Estiation o Haronic, Inharonic, and Tibral Structure and its Application to Source Sepatation NAOKI YASURAOKA and HIROSHI G. OKUNO 2 This paper presents a new ethod or polyphonic usic spectrogra odeling, The ethod decoposes polyphonic spectrogra into three types o actors: cobination o J tibral structures and K haronic structures, and L inharonic tibral structures. Haronic Gaussian unctions and an all-pole transer unction are introduced or representing haronic structure and tibral structure, respectively. The auxiliary unction ethod is used or estiating the odel paraeters, which consists o undaental requencies, allpole coeicients and volues o each eleent. A GUI designed or usical source separation with soe separation exaples is also introduced. Experiental result shows the proposed ethod separates each usical part ore accurately in coparison with another one based on nonnegative atrix actorization.. CD Haronic-Inharonic-Tibral Factorization: HITF HITF J K L K J + L J L Yaaha Corporation 2 Graduate School o Inoratics, Kyoto University c 202 Inoration Processing Society o Japan

信号全体で一定時間フレームごとに変化音量 Aplitude J 個 Frequency スペクトル包絡 K 個基本周波数 JK 個 + L 個 L 個 HITF GUI 2. HITF 2. 2 Short Tie Fourier Transor STFT Y φ Y φ n Y X X j, Y X := X j, j X j, := 2 HITF,3 5 2.

2 信号全体で一定時間フレームごとに変化音量 Aplitude J 個 Frequency スペクトル包絡 K 個基本周波数 JK 個 + L 個 L 個 HITF GUI 2. HITF 2. 2 Short Tie Fourier Transor STFT Y φ Y φ n Y X X j, Y X := X j, j X j, := 2 HITF, HITF HITF 2 n µ k n K G k J / A j L / B l n, j, k Hn j,k, l In l HITF X := j,k G k A j Hj,k n + l B l Il n 2 µ k n G k = exp ˆ ] hµ k n 2 h 3 2 c 202 Inoration Processing Society o Japan

3 h ˆ Hz σ 2 STFT 2 µ k n α j p, β l q A j := p αj pe i ˇp, B l := p βl qe i ˇp, i ˇ = 2π/F, F P, Q p, q P, Q 6 2 0,, 2,..., JK + L G k W, Un A j :=, k od K Hj,k n,, 0 < JK j /K B l, Il n, l JK, JK < JK + L od 2 X = W Un 6 JK + L W U n 4 5 HITF Nonnegative Matrix Factorization: NMF 7 NMF M H Un X := H Un 7 NMF 時間周波数解析部反復音響信号モデルパラメータ推定部 3 要素スペクトルの音量推定全極型伝達関数の係数推定調波音の基本周波数推定音源分離部 NMF 4 HITF {µ k n, α j p, β l q, U n } U n 0 Ũ n Ỹ Ỹ Y W Ũ n W U n Ỹ φ STFT 8 HITF 3. HITF 3. HITF Q iniize Q {Y }, {X } w.r.t. {µ k n, αp, j βq, l Un } 9 σ 2 STFT c 202 Inoration Processing Society o Japan

4 Q Q I Q I 9 Q I := Y log Y Y X X U n I µ k n 2 α j p, β l q IS 6 I 3.2 I 3.3 HITF 3.2 I I Y n Y γ A := γ p αpe i ˇp γ I Q I = Y log A γ + γ A γ γ 0 γ Y A 3 α p IS 6 α p Q I α p 2 7,0 2 α p Qθ Qθ = in Q + θ, ϑ 4 ϑ Q + θ, ϑ Q + ϑ θ Q + θ, ϑ θ, ϑ Q + 2 A 2 log A 2 2 log ρ + A 2 ρ = A 2 + 2ρ 2ρ 2 log ρ 5 2 log A 2 ρ ρ ρ A A 2 τ 2 Taylor A A τ τ 2 τ + 2 A τ 3 τ 2 = 2 A τ A τ τ τ A Newton τ 2 Q + Q + Y = A A 2ρ τ A τ 2 γ + C Y = + 2γ A 2ρ τ 3 2 5γ A τ 2 + C 7 C α p A α p 2 A 4 c 202 Inoration Processing Society o Japan

5 ω A Re ω A ], ω = 8 Re ] Q ++ A = η 5γω 2 ψ + C = η 2η τ 2 α p e η p η := Y + 2γ, ψ 2ρ τ 3 := η 5γω 2τ 2 α p 9 α p 3 ρ A 2, τ A, ω A A,q i ˇp 2 + C 9 9 α p 0 ] η α q e i ˇp q i ˇp = Re ψ e 22 p =,..., P α p α R 0 R P r α P R P R 0 r P ] R p := η e i ˇp i ˇp, r p := Re ψ e 24. Toeplitz, Levinson-Durbin. 3.3 HITF HITF Y 2, 6 HITF X 0 I Jensen log W Un λ log W U n λ λ n,, : λ > 0 n, : λ = Lagrange λ = W U n W U n 25 Q + = Y λ log W Un + W Un + C 27, C µ k n, α j p, β l q, U n 27 Un Un Q + Y λ = Un + W 28,, 0 Un, Y λ 29 U n, W αp j Y λ jk+k log A j + k,n Gk Hn j,k A j 30 j, k,n 2 j α j p 23 Y Y k,n λ jk+k γ k,n Gk Hn j,k βq l Y Y n λ JK+l γ n Il n αp j c 202 Inoration Processing Society o Japan

6 α j R j 0 R j P r j R j P R j 0 α j P Rp j := 2 A j 2 k,n rp j := Re 2 A j 2 k,n Y λ jk+k + 2 Y λ jk+k r j P A j 3 k,n + 4 5Aj 2 A j 3 A j G k H j,k n k,n ] i ˇp e ] ] G k Hn j,k i ˇp e 27 2 W Un 34, 2 = µ k n Y λ jk+k log exp ˆ hµ k n ] 2 k,j, Jensen log exp ˆ hµ k n ] 2 h h h ψ h,k ˆ hµ k n 2 log ψ h,k HITF. µ k n 3.4 U n αj p, βl q {Y } λ U n µ k n α j p, βl q U n 7. 2 h, k, n, : ψ h,k > 0 and n, : ψ h,k = 37 Q + = j,k,h, Y λ jk+k h,k ψ h,k ˆ hµ k n 2 + C 38 µ k n 0 µ k n j,h, h ˆY λ jk+k ψ h,k j,h, h2 Y λ jk+k ψ h,k 3.4 K U n GUI,4,5-6 c 202 Inoration Processing Society o Japan

4 HITF 2 3 4.. 2 2 / 2. 3 4 3 3. 3 + 3 5 3 4.

7 4 HITF / GUI Python HITF 5 HITF 3 Cython 2 CPU 2.5GHz kHz 6 5. J L 0 HITF NMF J 0 NMF F k-eans J 4 8, 0 7 c 202 Inoration Processing Society o Japan

8 2 HITF NMF Classic #37 Classic #39 Classic #42 SNR db: HITF=, NMF=. Violin Piano Piano Violin Harp Cello HITF NMF Jazz # Jazz #2 Jazz #4 Vibraphone Piano Piano Flute Piano Bass RWC Music Database: Jazz Music and Classic Music Standard MIDI File MIDI 44.kHz, STFT 2048, 52 P, Q 0 SNR j Y j, ξ X ξ, SNR j := ax 0 log Y 2 ] j, 0 ξ Y j, X ξ, 2 2 SNR Jazz # Jazz # 6. / HITF GUI NMF NMF 4 40, Saragdis, P. and Brown, J.: Non-negative atrix actorization or polyphonic usic transcription, Proc. WASPAA, pp Kaeoka, H., Nishioto, T. and Sagayaa, S.: Extraction o ultiple undaental requencies ro polyphonic usic using haronic clustering, Proc. ICA, pp.i Itoyaa, K., Goto, M., Koatani, K., Ogata, T. and Okuno, H.G.: Paraeter estiation or haronic and inharonic odels by using tibre eature distributions, IPSJ Journal, Vol.50, No.7, pp Vincent, E., Bertin, N. and Badeau, R.: Adaptive haronic spectral decoposition or ultiple pitch estiation, IEEE Trans. Audio, Speech and Lang. Process., Vol. 8, No. 3, pp Kaeoka, H., Ono, N., Kashino, K. and Sagayaa, S.: Coplex NMF: A new sparse representation or acoustic signals, Proc. ICASSP, pp Itakura, F. and Saito, S.: Analysis synthesis telephony based on the axiu likelihood ethod, Proc. ICA, pp.c 7 C Lee, D.D. and Seung, H.S.: Algoriths or non-negative atrix actorization, Proc. NIPS, pp Zhu, X., Beauregard, G.T. and Wyse, L.L.: Real-tie signal estiation ro odiied shorttie Fourier transor agnitude spectra, IEEE Trans. Audio, Speech and Lang. Process., Vol.5, No.5, pp FitzGerald, D., Cranitch, M. and Coyle, E.: On the use o the beta divergence or usical source separation, Proc. ISSC, pp Kaeoka, H., Ono, N. and Sagayaa, S.: Auxiliary unction approach to paraeter estiation o constrained sinusoidal odel or onaural speech separation, Proc. ICASSP, pp Levinson, N.: The Wiener RMS error criterion in ilter design and prediction, Journal o Matheatical Physics, Vol.25, pp Seljebotn, D.S.: Fast nuerical coputations with Cython, Proc. Scipy Goto, M., Hashiguchi, H., Nishiura, T. and Oka, R.: RWC usic database: popular, classical, and jazz usic databases, Proc. ISMIR, pp Nakano, M., Roux, J.L., Kaeoka, H., Kitano, Y., Ono, N. and Sagayaa, S.: Nonnegative atrix actorization with Markov-chained bases or odeling tie-varying patterns in usic spectrogras, Proc. LVA/ICA c 202 Inoration Processing Society o Japan

IPSJ SIG Technical Report Vol.2014-MUS-104 No /8/27 F0 1,a) 1,b) 1,c) 2,d) (F0) F0 F0 Graphical User Interface (GUI) F0 1. [1] CD MIDI [2] [3,

IPSJ SIG Technical Report Vol.2014-MUS-104 No /8/27 F0 1,a) 1,b) 1,c) 2,d) (F0) F0 F0 Graphical User Interface (GUI) F0 1. [1] CD MIDI [2] [3, F,a),b),c) 2,d) (F) F F Graphical User Interface (GUI) F. [] CD MIDI [2] [3, 4] [5] 2 a) ikemiya@kuis.kyoto-u.ac.jp b) itoyama@kuis.kyoto-u.ac.jp c) yoshii@kuis.kyoto-u.ac.jp d) okuno@aoni.waseda.jp TANDEM-STRAIGHT