tailieunhanh - EURASIP Journal on Applied Signal Processing 2003:10, 953–967 c 2003 Hindawi Publishing

EURASIP Journal on Applied Signal Processing 2003:10, 953–967 c 2003 Hindawi Publishing Corporation Frequency-Zooming ARMA Modeling for Analysis of Noisy String Instrument Tones Paulo A. A. Esquef Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, . Box 3000, FIN-02015 HUT, Espoo, Finland Email: Matti Karjalainen Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, . Box 3000, FIN-02015 HUT, Espoo, Finland Email: ¨ ¨ Vesa Valimaki Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, . Box 3000, FIN-02015 HUT, Espoo, Finland Pori School of Technology and Economics, Tampere University of Technology, . Box 300, FIN-28101 Pori, Finland. | EURASIP Journal onApplied Signal Processing 2003 10 953-967 2003 Hindawi Publishing Corporation Frequency-Zooming ARMA Modeling for Analysis of Noisy String Instrument Tones Paulo A. A. Esquef Laboratory of Acoustics and Audio Signal Processing Helsinki University of Technology P O. Box 3000 FIN-02015 HUT Espoo Finland Email paulo. esquef@ Matti Karjalainen Laboratory of Acoustics and Audio Signal Processing Helsinki University of Technology P O. Box 3000 FIN-02015 HUT Espoo Finland Email Vesa Valimaki Laboratory of Acoustics and Audio Signal Processing Helsinki University of Technology P O. Box 3000 FIN-02015 Hut Espoo Finland Pori School of Technology and Economics Tampere University of Technology P O. Box 300 FIN-28101 Pori Finland Email Received 31 May 2002 and in revised form 5 March 2003 This paper addresses model-based analysis of string instrument sounds. In particular it reviews the application of autoregressive AR modeling to sound analysis synthesis purposes. Moreover a frequency-zooming autoregressive moving average FZ-ARMA modeling scheme is described. The performance of the FZ-ARMA method on modeling the modal behavior of isolated groups of resonance frequencies is evaluated for both synthetic and real string instrument tones immersed in background noise. We demonstrate that the FZ-ARMA modeling is a robust tool to estimate the decay time and frequency of partials of noisy tones. Finally we discuss the use of the method in synthesis of string instrument sounds. Keywords and phrases acoustic signal processing spectral analysis computer music sound synthesis digital waveguide. 1. INTRODUCTION It has been known for quite a long time that a free vibrating body may generate a sound that is composed of damped sinusoids assuming valid the hypothesis of small perturbations and linear elasticity 1 . This behavior has motivated the use of a set of controllable sinusoidal oscillators to artificially emulate the

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