Simulating Pluck/Strike Position

From string acoustics, we know that a string plucked at 1/th the distance from one end will not have energy at the th partial and its integer multiples.
If we initialize the delay lines of a waveguide model with a particular plucked string shape, the pluck position “filtering” is automatically included (it's defined by the initial energy profile that is defined by the initial shape).
In practice, however, it is common that the delay lines are either initialized with noise or driven with an external input signal (in which case they are initialized with zeros).
Pluck position filtering can be simulated with a feedforward comb filter, which creates notches in the frequency magnitude response at equal frequency intervals.

Figure 7: A feedforward comb filter block diagram.
$\begin{figure}\begin{center} \begin{picture}(3.9,0.8) \put(0.27,0){\epsfig{fil... ...0.67){$b_{0}$} \put (3.9,0.12){$y[n]$} \end{picture} \end{center} \end{figure}$

Figure 8: Magnitude response of a feedforward comb filter with , $b_{0} = 1$ , and $g = b_{M}$ = 0.1, 0.5, and 0.9.
$\begin{figure}\begin{center} \epsfig{file=figures/mag-forward-comb.eps, width=3.5in} \end{center} \end{figure}$
For $b_{M} > 0$ , there are peaks in the frequency response, centered about the frequencies $\omega_{k} = 2 \pi k/M, k = 0, 1, \ldots, M-1$ . Between these peaks, there are notches at intervals of $f_{s}/M$ Hz.