Extended Karplus-Strong (EKS) Algorithm

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