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The wave digital (WD) tonehole model closely approximates the tonehole transmission-line model described in [3]. This was verified by comparing the reflection function of a six-hole flute, as computed in [3], with the reflection function of a WD model of the flute. Figure 5 displays this comparison for a fingering that corresponds to the note G. A 5kHz low-pass filter was applied to both reflection functions in order to facilitate a visual comparison. In the WD model, fractional delay-lengths were modelled using third-order Lagrange interpolation filters [5], which have a negligible error in a bandwidth of 5kHz. In order to further ensure that the comparison is focussed on the tonehole part of the model, viscothermal losses were neglected in both computations.
Figure 5:
Six-hole flute reflection function for the note G (the first three holes closed).
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Note that the fit is so close that the difference between the curves is barely visible.
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Download wdth.pdf