### The Extended Karplus-Strong Algorithm

Figure 9.2 shows a block diagram of the *Extended Karplus-Strong* (EKS)
algorithm [207].

The EKS adds the following features to the KS algorithm:

where

Note that while can be used in the tuning allpass, it is better to offset it to to avoid delays close to zero in the tuning allpass. (A zero delay is obtained by a pole-zero cancellation on the unit circle.) First-order allpass interpolation of delay lines was discussed in §4.1.2.

A history of the Karplus-Strong algorithm and its extensions is given in §A.8. EKS sound examples are also available on the Web. Techniques for designing the string-damping filter and/or the string-stiffness allpass filter are summarized below in §6.11.

An implementation of the Extended Karplus-Strong (EKS) algorithm in the Faust programming language is described (and provided) in [454].

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