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 http://ccrma.stanford.edu/~jos/pasp/Ideal_Plucked_String.html.