One-Zero String Damping Filter

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One-Zero String Damping Filter

The original EKS string-damping filter replaced the two-point average of the KS digitar algorithm by a weighted two-point average

$\displaystyle H_d(z) = (1-S) + Sz^{-1} \protect$

(D.2)

where $S\in[0,1]$ is called the ``stretching factor,'' and it adjusts the relative decay-rate for high versus low frequencies in the string. This filter goes in the string feedback loop, as shown in Fig.D.4 above. At

, the decay time is ``stretched infinitely'' (no decay), while fastest decay is obtained when

, where it reduces to the KS digitar damping filter. The decay-time is always infinity for dc, and higher frequencies decay faster than lower frequencies when $S\in(0,1)$ .

To control the overall decay rate, another (frequency-independent) gain multiplier $\rho\in(0,1)$ was introduced to give the loop filter

$\displaystyle H_d(z) = \rho[(1-S) + Sz^{-1}].$

Since this filter is applied once per period

at the fundamental frequency, an attenuation by the factor $\vert H_d(e^{j2\pi/P})\vert\approx\rho$ occurs once each

samples. Setting $\rho$ to achieve a decay of

dB in

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Chapters

Physical Audio Signal Processing
    Making Virtual Electric Guitars and Guitar Effects Using Faust and Octave
       Extended Karplus-Strong Algorithm
          One-Zero String Damping Filter