Statistical data modeling approach for determining the acoustic impedance of musical instruments Free

Recent theoretical models [M. E. McIntyre et al., J. Acoust. Soc. Am. 74, 1325–1345 (1983)] for the oscillation mechanism of musical instruments have utilized an analytic closed‐form relationship between the Green's function g(t), the reflection function r(t), and the acoustic impedance Z₀ (which may also be time varying). Given two of the three quantities {g(t), r(t), Z₀}, the method used to find the third function usually involves the discrete Fourier transform. This paper presents an alternate approach to the problem of estimating Z₀ from measurements of g(t) and r(t). Statistical data modeling in the context of digital filter design provides a solution that does not require the computation of a discrete Fourier transform. It is shown that the acoustic impedance is the impulse response of the cascade of two digital filters whose coefficients minimize the fitting error between an (M,N)th order model and the observed sequences.