Estimation of Modal Decay Parameters from Noisy Response Measurements*

Parametric analysis, modeling, and equalization (inverse modeling) of reverberant and resonating systems find many applications in audio and acoustics. These include room and concert hall acoustics, resonators in musical instruments, and resonant behavior in audio reproduction systems. Estimating the reverberation time or the modal decay rate are important measurement problems in room and concert hall acoustics [1], where signal-to-noise ratios (SNRs) of only 30–50 dB are common. The same problems can be found, for example, in the estimation of parameters in model-based sound synthesis of musical instruments, such as vibrating strings or body modes of string instruments [2]. Reliable methods to estimate parameters from noisy measurements are thus needed. In an ideal case of modal behavior, after a possible initial transient, the decay is exponential until a steady-state noise floor is encountered. The parameters of primary interest to be estimated are