Time-domain simulation of acoustical waveguides with arbitrarily spaced discontinuities

The multiconvolution algorithm [Martinez et nl., J. Acoust. Sec. Am. 84, 16 20-1627 (1988)] to calculate the impulse response or reflection function of a musical instrument air column has proved to be useful, but it has the li mitation that the spacing between discontinuites is constrained to be some multiple of c Delta t (for phase velocity c and time step c Delta t). This paper presents an improved method, the continuous-time interpolated multico nvolution (CTIM): where such a limitation has been removed. The response of an air column, modeled as an arbitrary one-dimensional acoustic waveguide constructed using cylindrical or conical bore segments with viscothermal da mping and tone-hole discontinuities, is obtained through continuous-time co nvolutions between analytical reflection and transmission functions and dis crete-time pressure signals. The arbitrary spacing between discontinuites i s accounted for by interpolation of the discrete-time pressure signals. Man y musical instrument air columns possess tone holes that are opened or clos ed so that tones of different pitches are produced. A time-domain calculati on is presented of the acoustic responses of tone-hole discontinuities that may be open or closed. The resulting reflection and transmission functions are well suited for use in the CTIM. (C) 1999 Acoustical Society of Americ a. [S0001-4966(99)01502-7].