Sinusoidal modeling

Another way to find the least-damped mode parameters is by means of an intermediate sinusoidal model of the body impulse response, or, more appropriately, the energy decay relief (EDR) computed from the body impulse response (see §2.2.2). Such sinusoidal models have been used to determine the string loop filter in digital waveguide strings models. In the case of string loop-filter estimation, the sinusoidal model is applied to the impulse response (or ``pluck'' response) of a vibrating string or acoustic tube. In the present application, it is ideally applied to the EDR of the body impulse response (or ``hammer-strike'' response).

Since sinusoidal modeling software (e.g. [432]) typically quadratically interpolates the peak frequencies, the resonance frequencies are generally quite accurately estimated provided the frame size is chosen large enough to span many cycles of the underlying resonance.

The sinusoidal amplitude envelopes yield a particularly robust measurement of resonance bandwidth. Theoretically, the modal decay should be exponential. Therefore, on a