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Theoretical Plucks

If we want an impulse at the sampling distance of where the pluck position of the guitar would be, we calculate $ X$ such that the samples for each delay line tapped into correspond to the same physical location of the instrument [19]. We then set $ e(0)=1$ and $ e(n)=0$ for all $ n > 0$ .

As Karplus-Strong discussed, exciting a digital waveguide with an impulse is psychoacoustically plain, whereas exciting the digital waveguide with random values results in a more satisfying sound [20].

With delay lines modeling displacement, we can linearly-interpolate between the pluck-point to the two ends of the string for both traveling waves for an excitation that displaces the string at a single point causing the remainder of the string to displace linearly to the ends of the string. Furthermore, if the delay lines represent acceleration or curvature, this ideal-pluck is a single non-zero sample in each delay line. Note, since the digital waveguide is a sampled model of a continuous system, band-limiting conditions need be accounted for. A detailed description of such can be found in

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Download phys_mod_overview.pdf

``Virtual Stringed Instruments'', by Nelson Lee and Julius O. Smith III,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-02-20 under the Creative Commons License (Attribution 2.5), by Nelson Lee and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University