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Articles - CCRMA - Stanford University

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Freeverb Allpass Approximation<br />

Schroeder Diffusion Allpass<br />

Freeverb implements<br />

AP g<br />

N<br />

AP g<br />

N<br />

∆<br />

= −g +z−N<br />

1−gz −N<br />

≈ −1+(1+g)z−N<br />

1−gz −N<br />

• Each Freeverb “allpass” is more precisely a feedback<br />

in series with a feedforward<br />

comb-filter FBCF g<br />

N<br />

comb-filter FFCF −1,1+g<br />

N , where<br />

FBCF g<br />

N<br />

FFCF −1,1+g<br />

N<br />

∆<br />

=<br />

1<br />

1−gz −N<br />

∆<br />

= −1+(1+g)z −N .<br />

• A true allpass is obtained at g = ( √ 5−1)/2 ≈ 0.618<br />

(reciprocal of “golden ratio”)<br />

• Freeverb default is g = 0.5<br />

27

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