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1 GUI Selective Amplifier of Periodic and Non-periodic Components in Concurrent Audio Signals with Spectral Control Envelopes Hirokazu Kameoka Masataka Goto Shigeki Sagayama Graduate School of Information Science and echnology, he University of okyo National Institute of Advanced Industrial Science and echnology (AIS Abstract We propose a new equalizing technique that enables a separate control of periodic and non-periodic source components in music signals through a spectral mapping using the two spectral control envelopes. he applications we have in mind are for example a selective amplifier of drum sounds and other instruments in a polyphonic music signal and a recuperation of a degraded music signal with an additive white noise. ( iunes WinAmp [] ( INER:D [7] Drumix [8] [9]

jp GUI Selective Amplifier of Periodic and Non-periodic Components in Concurrent Audio Signals with Spectral Control Envelopes Hirokazu Kameoka Masataka Goto Shigeki Sagayama Graduate School of

2 Amplitude (db 3 error g(ω;a log g(ω;a log < log g(ω;a ( g(ω;a g(ω;a g(ω;a log g(ω;a log > log g(ω;a Amplitude (db log log g(ω;a log log g(ω; a log log g(ω; a log log g(ω; a [, 3, 4, 5, 6] (Linear Predictive Coding LPC LPC i : a i > g(ω; a = ( a = (a,, a I Ψ i (ω ω R < Ψ i (ω < ( Ψ i (ω Gauss Ψ i (ω ( Gauss a = (a,, a I 3 3. a LPC []

5-4 -3 - - 3 4 log log g(ω;a log log g(ω; a log log g(ω; a log log g(ω; a 3 4 8.

3 f (x f (x: convex function f(tx(-tx t f(x(-t f(x ω : m i (ω =, i, ω : < m i (ω < (6 x 3 tx(-tx [] = ( g(ω; a log g(ω; a dω (3 = ( g(ω; a log g(ω; a x x dω (4 log log g(ω; a ( (3 (4 3. a a ω : ai Ψ i (ω log m i (ω = log m i (ω log m i (ω m i (ω x j wj x j w j j w jx j 3 ( ( ai Ψ i (ω log m i (ω log m i (ω dω (7 m [m ] m i (ω [m ] a i ( a i a i a i m i (ω (7 a i (7 [m ] m i (ω a i 4 (6 [m ] m i (ω ( = log log dω (5 a EM a ( m i (ω log m i (ω log m i (ω ( λ(ω m i (ω dω (8 log m i (ω λ(ω (9 m i (ω λ(ω Lagrange (9 m i (ω m i (ω = a iψ i (ω eλ(ω (

a a ω : ai Ψ i (ω log m i (ω = log m i (ω log m i (ω m i (ω x j wj x j w j j w jx j 3 ( ( ai Ψ i (ω log m i (ω log m i (ω dω (7 m [m ] m

4 [m ] m [m ] [m ] a [m ] 4 a i m i (ω m i (ω ( a i ( (6 m i (ω = a iψ i (ω i ( i:a i > ω :Ψ(ω> i, ω : m i (ω > m i (ω a i a i ( Ψi (ω m i (ω dω ( a i m i (ωdω â i = Ψi (ω dω (3 i, ω : m i (ω > i : â i > i : a i ( (3 a a a 3.3 a P (a η i a i a i (4 a i a i P (a a i ( i : η i a ( = i a iψ i (ω log log dω P (a (5 a a a a ω : m i (ω =, i, ω : < m i (ω < (6 / ai Ψ i (ω ω : m i (ω m i (ω = i / ai Ψ i (ω m i (ω = m i (ω m i (ω ( m i (ω log a i Ψ i (ω log dω P (a (7 [m ] ω log (8 t(ω log t(ω ( t(ω t(ω (9 (7 ( m i (ω log t(ω log a i Ψ i (ω ( t(ω dω P (a ( t(ω

3 a P (a η i a i a i (4 a i a i P (a a i ( i : η i a ( = i a iψ i (ω log log dω P (a (5 a a a a ω : m i (ω =, i, ω : < m i (ω < (6 / ai Ψ

5 [m, t] [ m ] [ m, t ] ( [m, t] m i (ω t(ω a ( m i (ω t(ω m i (ω ( ( ( m i (ω γ(ω m i (ω dω m i (ω m i (ω γ(ω ( m i (ω γ(ω Lagrange ( m i (ω m i (ω = γ(ωa iψ i (ω (6 m i (ω = a iψ i (ω i (3 (4 i:a i > ω :Ψ(ω> i, ω : m i (ω > m i (ω (7 = [m ] t(ω = (5 [m ] = [m, t] m i (ω t(ω (4 (5 = [m, t] m i (ω t(ω a ( a i ( Ψi (ω t(ω m i (ω Ψ i (ω a i dω η ia i a i ω : <t(ω, Ψ i (ω< m i (ω dω η i a i ã i = Ψ i (ω Ψi (ω t(ω dω / (6 (7 ã a a i a i a i {ãi if ã i : â i = i a i a i otherwise (8 [m ] [m ] m [m, t] [m, t] a [m ] t [m, t] [m, t ] [m ] [m ] [m, t ] [m, t ] [m, t ] a 5 a i m i (ω t(ω m i (ω t(ω ( a i ( i, ω : m i (ω > i : â i > i : a i (4 (5 (7 ( 5 a a 4 ε(> log log log ε log ε log ω log log

i a i ω : <t(ω, Ψ i (ω< m i (ω dω η i a i ã i = Ψ i (ω Ψi (ω t(ω dω / (6 (7 ã a a i a i a i {ãi if ã i : â i = i a i a i otherwise (8 [m ] [m ] m [m, t] [m, t] a [m ] t [m,

log log g(ω; a g(ω; a log g(ω; a log g(ω; a log g(ω; a g(ω; a log g(ω; a log = log 8. ime (s 4. 8. ime (s 4. log g(ω; a log g(ω; a log g(ω; a g(ω; a log g(ω; a log Amplitude (db 6 log log log 8.

6 log log g(ω; a g(ω; a log g(ω; a log g(ω; a log g(ω; a g(ω; a log g(ω; a log = log 8. ime (s ime (s 4. log g(ω; a log g(ω; a log g(ω; a g(ω; a log g(ω; a log Amplitude (db 6 log log log 8. log log log ( 6 g(ω; a g(ω; a g(ω; ā g(ω; ā log log log = log g(ω; ā log g(ω; ā g(ω; a g(ω; a g(ω; a g(ω; ā ( log f log g(ω; a g(ω; a α ( log g(ω; a log g(ω; a (9 f( sigmoid { (x f(x = e x = (x (3 α log log g(ω; ā g(ω; a log if log = log g(ω; a g(ω; a log log g(ω; ā g(ω; a if log < log g(ω; a g(ω; a ( ( GUI GUI 6kHz 6ms Hamming 8ms Fourier 3 i 4 ihz 4Hz a,, a dω η α η i =./i (i =,, α =. MALAB 7 GUI 6 i =, i = 3, 4, 5 i = 6, 7, 8 i = 9,,, i = 3, 4, 5, 6 i = 7, 8, 9, 4 GUI 8 RWC [] GUI

log log log ( 6 g(ω; a g(ω; a g(ω; ā g(ω; ā log log log = log g(ω; ā log g(ω; ā g(ω; a g(ω; a g(ω; a g(ω; ā ( log f log g(ω; a g(ω; a α ( log g(ω; a log g(ω; a (9 f( sigmoid

7 8. 6 GUI GUI ime (s ime (s 9 RWC [] ive (Piano Solo ( ( ( PROLOGUE,, RWC-MDB-P- No.7 Lounge Away, YOU Band, RWC-MDB-- No.8 RWC [] ive (Piano Solo,, RWC-MDB-- No. 9 ( [] Rose,., Audio Postproduction for Digital Video (Dv Expert Series, CMP Books,. [] M. N. S. Swamy and K. S. hyagarajan, Digital Bandpass and Bandstop Filters with Variable Center Frequency and Bandwidth, Proc. IEEE, Vol. 64, pp , 976. [3] S. Erfani and B. Peikari, Variable Cutt-off Digital Ladder Filters, Int.. Electron., Vol. 44, pp , 978. [4] E. C. an, Variable Lowpass Wave-digital Filters, Electron. Lett., Vol. 8, pp , 98. [5] P. A. Regalia and S. K. Mitra, unable Digital Frequency Response Equalization Filters, IEEE rans. Acoust., Speech, Signal Process., ASSP-35, No., pp. 8, 987. [6] S.. Orfanidis, Digital Parametric Equalizer Design with Prescribed Nyquist-frequency Gain, ournal of the Audio Engineering Society, Vol. 45, No. 6, pp , 997. [7] Yoshii, K., Goto, M. and Okuno, H. G., INER:D: A Drum Sound Equalizerfor Controlling Volume and imbre of Drums, In Proc. nd European Workshop on the Integration of Knowledge, Semantic and Digital Media echnologies (EWIM5, 5. [8],,,,, Drumix:, 6, 6. [9] Yoshii, K., Goto, M., Komatani, K., Ogata,., Okuno, H. G., An Error Correction Framework based on Drum Pattern Periodicity for Improving Drum Sound Detection, In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP6, 6. [],,,, 97. [],,,, RWC :,, Vol.45, No.3, pp , 4.

IEEE, Vol. 64, pp. 63 634, 976. [3] S. Erfani and B. Peikari, Variable Cutt-off Digital Ladder Filters, Int.. Electron., Vol. 44, pp. 535 549, 978. [4] E. C. an, Variable Lowpass Wave-digital Filters, Electron.

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