Dynamic Level Lowpass Filter

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Dynamic Level Lowpass Filter

In real strings, the spectral centroid typically rises as plucking/striking becomes more energetic. The EKS dynamic-level lowpass filter (diagrammed at the far right in Fig.D.4) qualitatively models this phenomenon:^D.7

$\displaystyle H_{L,\omega_1}(z) \eqsp \frac{1-R_L}{1 - R_Lz^{-1}}$

This is another unity-dc-gain one-pole lowpass, with a pole at $z=R_L\in[0,1)$ set such that the gain is the same for all fundamental frequencies [213]. Here we will derive simplified design formulas.

Assume that the ideal continuous-time filter has the transfer function

$\displaystyle H_{L,\omega_1}(s) = \frac{\omega_1}{s+\omega_1} \protect$

(D.3)

where $\omega_1 = 2\pi f_1$ denotes the fundamental frequency in radians per second. This lowpass filter has unity dc gain,

dB gain at $s=j\omega_1$ , and rolls off

dB/octave for $\omega\gg\omega_1$ .^D.8It also happens to be the 1st-order Butterworth lowpass with cut-off frequency set to $\omega_1$ rad/sec. To achieve the dynamic level effect, the output of this filter is linearly panned with its input. If

denotes the lowpass input

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Physical Audio Signal Processing
    Making Virtual Electric Guitars and Guitar Effects Using Faust and Octave
       Extended Karplus-Strong Algorithm
          Dynamic Level Lowpass Filter