Analysis and resynthesis of the trumpet bore

Experimental studies of impulse responses in a trumpet bore have suggested a divide‐and‐conquer approach in which the contributions of the major elements (input end, uniform pipe, and output end) can be examined and understood separately. Multiple convolutions are then used to assemble these into the time‐domain response (Green's function) of the complete instrument. The resynthesis is most easily understood for simpler structures in which the input end can be modeled adequately by lumped elements. Spatially extended input ends are handled by a more complicated formalism involving transmission impulse responses, but the spirit of the calculation is the same. Fourier transforming this work allows us to untangle partially the contributions of the major elements to the input impedance function of the complete instrument. [Work supported by a CSULB Summer Res. Grant and Equipment Grants from Hewlett‐Packard. Special thanks are also due to Lowell J. Eliason for his long‐term support of the experimental work and to William T. Cardwell, Jr. for our continuing dialogue on what is really happening in a trumpet's bore.]