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Damping Filter Design The damping filter Gi(z) associated with the delay line of length Mi in the FDN can be written in principle as Gi(z) = G Mi T (z)Li(z) where GT(z) is the lowpass filter corresponding to one sample of wave propagation through air, and Li(z) is a lowpass corresponding to absorbing/scattering boundary reflections along the (hypothetical) ith propagation path. Define t60(ω) = desired reverberation time at frequency ω pk = e jω kT = kth pole of the lossless prototype We can introduce frequency-independent damping with the (conformal map) substitution z −1 ← gz −1 • This z-plane mapping pulls all poles in the z plane from the unit circle to the circle of radius g • Pole pk = e jω kT moves to ˜pk = ge jω kT 34
Example • Start with a pole at dc (digital integrator): H(z) = 1 ↔ [1,1,1,...] 1−z −1 • Move it from radius 1 to radius 0.9 using z−1 ← 0.9z−1 : 1 H(z) = ↔ [1,0.9,0.81,...] 1−0.9z −1 35
Page 1 and 2: MUS420/EE367A Lecture 3 Artificial
Page 3 and 4: Implementation Let hij(n) = impulse
Page 5 and 6: Possibility of a Physical Reverb Mo
Page 7 and 8: Perception of Echo Density and Mode
Page 9 and 10: Proof that Mode Density Grows as Fr
Page 11 and 12: Perceptual Metrics for Ideal Reverb
Page 13 and 14: Energy Decay Relief (EDR) The energ
Page 15 and 16: x(n) Reverb = Early Reflections + L
Page 17 and 18: Desired Qualities: Late Reverberati
Page 19 and 20: Schroeder Allpass Sections (Late Re
Page 21 and 22: Are Allpass Filters Really Colorles
Page 23 and 24: • Schroeder suggests a progressio
Page 25 and 26: • d (“damping”) default: Free
Page 27 and 28: Freeverb Allpass Approximation Schr
Page 29 and 30: Choice of Orthogonal Feedback Matri
Page 31 and 32: Choice of Delay Lengths Mi • Dela
Page 33: u(n) b3 b2 b1 Choice of Loss Gains
Page 37 and 38: Lossy Mapping Let’s in more detai
Page 39 and 40: Desired Pole Radius Pole radius Rk
Page 41 and 42: Tonal Correction Filter Let hk(n) =
Page 43 and 44: Zita-Rev1 Damping Filters FDN rever
Page 45 and 46: Rectilinear Digital Waveguide Mesh
Page 47: Reverb Resources on the Web • Har

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