Estimating Waveguide Model Elements from Acoustic Tube Measurements

One-dimensional digital waveguides are widely used to model traveling pressure waves along wind instrument bores comprised of concatenated cylindrical or conical sections. Waveguide filter elements model frequencydependent losses and delay (dispersion) occurring during propagation and at any boundary or discontinuity producing reflected and transmitted waves. In this work, a technique is described for estimating wind instrument waveguide elements from several measurements of the system’s impulse response, each measurement taken with the system having incrementally varying termination/boundary conditions. The measured impulse responses yield sequences of multiple arrivals from which estimates of waveguide element transfer functions may be formed. The measurement and post signal processing technique is explored using simple structures consisting of cylindrical and conical tubes, as these are well described theoretically and provide a basis for validating measured data. All waveguide elements necessary for modeling typical wind instrument bores are collected here, each presented with a theoretical description and accompanying measurement. The measurement and processing system is then shown to yield data closely matching the theory, thus providing confidence that the technique may be extended to accurately measure structures which are more difficult to describe theoretically, such as an instrument’s flaring bell.