Matti Karjalainen
Vesa Välimäki
Jyri Huopaniemi
Zoltan Janosy
At the HUT Acoustics Laboratory we have studied simulation of a vibrating string for several years. This work has led to the development of a synthesis model for the acoustic guitar. The sound quality of our digital guitar synthesizer is very good: an average listener cannot distinguish it from a sound of an acoustic instrument.
The guitar model is based on the waveguide modeling approach where each string is simulated using a delay line loop. Inside this loop, a simple digital lowpass filter brings about the frequency-dependent losses needed to imitate the attenuation of vibration in a physical string.
Recently, we have concentrated on the calibration of the model parameters according to a recording of a guitar tone. The sound signal is analyzed using the short-term Fourier transform and the time-varying envelope of each harmonic component is detected. Each of these envelope curves is approximated with a straight line minimizing the least-squares error criterion. The slopes of these lines determine the loop gain at the harmonic frequencies. The coefficients of the loop filter are matched to these data.
The excitation signal to the string model is obtained by inverse filtering the digitally recorded guitar sound. The signal is fed into the inverse transfer function of the string model. In the output, the harmonic components have vanished and the residual is a signal that decays rapidly. We truncate (using the left wing of a window function) the first 100 ms of the residual and use that as the excitation signal. The same excitation signal can be used for other tones as well since the main contribution of the excitation is to provide the impulse response of the wooden body in the synthetic sound.
We have used the same approach to synthesize other plucked string instruments, such as the steel-string guitar, the mandolin, and the banjo. We are also planning to implement a real-time synthesis model of a traditional Finnish string instrument, the kantele, which is an ancient zither. The strings of the kantele have been attached in a special way that causes beats and nonlinear effects to the sound. These phenomena are characteristic to the sound of kantele and have to be included in the synthesis model.
An audio example played by the Acoustics Lab guitar synthesizer is available in the sound demos-section of our WWW server.
Matti Karjalainen and Vesa Välimäki, "Model-based analysis/synthesis of the acoustic guitar," in Proc. Stockholm Music Acoustics Conf. (SMAC 93), pp. 443-447, Stockholm, Sweden, July 28-Aug. 1, 1993, published in Oct. 1994. Audio examples included on the SMAC 93 CD.
Vesa Välimäki, Jyri Huopaniemi, Matti Karjalainen, and Zoltan Janosy, "Physical Modeling of Plucked String Instruments with Application to Real-Time Sound Synthesis," J. Audio Eng. Soc., vol. 44, no. 5, pp. 331-353, May 1996.