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Extended Karplus-Strong (EKS) Algorithm

\epsfig{file=eps/eks.eps,width=\textwidth }

\begin{eqnarray*}
N &=& \mbox{pitch period ($2\times$\ string length) in samples}\\ [10pt]
H_p(z) &=& \frac{1-p}{1 - p\,z^{-1}} = \mbox{pick-direction lowpass filter}\\ [10pt]
H_\beta(z) &=& 1 - z^{-\beta N} = \mbox{pick-position comb filter, $\beta\in(0,1)$}\\ [10pt]
H_d(z) &=& \mbox{string-damping filter (one/two poles/zeros typical)}\\ [10pt]
H_s(z) &=& \mbox{string-stiffness allpass filter (several poles and zeros)}\\ [10pt]
H_\rho(z) &=& \frac{\rho(N)-z^{-1}}{1 - \rho(N)\,z^{-1}} = \mbox{first-order string-tuning allpass filter}\\ [10pt]
H_L(z) &=& \frac{1-R_L}{1 - R_L\,z^{-1}} = \mbox{dynamic-level lowpass filter}
\end{eqnarray*}



Subsections
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``Elementary Digital Waveguide Models for Vibrating Strings'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-04-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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