### The Karplus-Strong Algorithm

The simulation diagram for the ideal string with the simplest frequency-dependent loss filter is shown in Fig. 9.1. Readers of the computer music literature will recognize this as the structure of the*Karplus-Strong algorithm*[236,207,489].

*per se,*is obtained when the delay-line initial conditions used to ``pluck'' the string consist of random numbers, or ``white noise.'' We know the initial

*shape*of the string is obtained by

*adding*the upper and lower delay lines of Fig. 6.11,

*i.e.*, . It is shown in §C.7.4 that the initial

*velocity*distribution along the string is determined by the

*difference*between the upper and lower delay lines. Thus, in the Karplus-Strong algorithm, the string is ``plucked'' by a

*random initial displacement and initial velocity distribution.*This is a very energetic excitation, and usually in practice the white noise is lowpass filtered; the lowpass cut-off frequency gives an effective

*dynamic level*control since natural stringed instruments are typically brighter at louder dynamic levels [428,207]. Karplus-Strong sound examples are available on the Web. An implementation of the Karplus-Strong algorithm in the Faust programming language is described (and provided) in [454].

**Next Section:**

The Extended Karplus-Strong Algorithm

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One-Zero Loop Filter