PHYSICAL AUDIO SIGNAL PROCESSING
FOR VIRTUAL MUSICAL INSTRUMENTS AND AUDIO EFFECTS

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA

August 2007 Edition

• Preface
  • Book Series Overview
  • Acknowledgments
  
  
• Acoustic Modeling with Delay
  • Delay Lines
    • A Software Delay Line
  • Acoustic Wave Propagation Simulation
    • Traveling Waves
    • Damped Traveling Waves
    • Converting Propagation Distance to Delay Length
    • Spherical Waves from a Point Source
    • Reflection of Spherical or Plane Waves
    • An Acoustic Echo Simulator
    • Program for Acoustic Echo Simulation
  • Lossy Acoustic Propagation
    • Exponentially Decaying Traveling Waves
    • Dispersive Traveling Waves
    • Summary
  • Digital Waveguides
    • Physical Outputs
  • Tapped Delay Line (TDL)
    • Example Tapped Delay Line
    • Transposed Tapped Delay Line
    • TDL for Parallel Processing
    • General Causal FIR Filters
  • Comb Filters
    • Feedforward Comb Filters
    • Feedback Comb Filters
    • Feedforward Comb Filter Amplitude Response
    • Feedback Comb Filter Amplitude Response
    • Filtered-Feedback Comb Filters
    • Equivalence of Parallel Combs to TDLs
    • Equivalence of Series Combs to TDLs
    • Time Varying Comb Filters
  • Feedback Delay Networks (FDN)
    • FDN and State Space Descriptions
    • Single-Input, Single-Output (SISO) FDN
    • FDN Stability
  • Allpass Filters
    • Allpass from Two Combs
    • Nested Allpass Filters
    • More General Allpass Filters
    • Example Allpass Filters
    • Gerzon Nested MIMO Allpass
  • Allpass Digital Waveguide Networks
    • Signal Scattering
    • Digital Waveguide Networks
  • Comb-Filter Problems
  • FDN Problems
  
  
• Artificial Reverberation
  • The Reverberation Problem
    • Exact Reverb via Transfer-Function Modeling
    • Complexity of Exact Reverberation
    • Possibility of a Physical Reverb Model
  • Perceptual Aspects of Reverberation
    • Perception of Echo Density and Mode Density
    • Perceptual Metrics for Ideal Reverberation
      • Energy Decay Curve
      • Energy Decay Relief
  • Early Reflections
  • Late Reverberation Approximations
    • Desired Qualities in Late Reverberation
    • Schroeder Allpass Sections
    • Nested Allpass Filters
  • A Schroeder Reverberator called JCRev
  • Freeverb
    • Freeverb Main Loop
    • Moorer Lowpass Feedback Comb Filter
    • Freeverb Allpass Approximation
    • Conclusions
  • FDN Reverberation
    • History of FDNs for Artificial Reverberation
    • Choice of Lossless Feedback Matrix
      • Householder Feedback Matrix
      • Most General Lossless Feedback Matrices
      • Triangular Feedback Matrices
    • Choice of Delay Lengths
      • Mean Free Path
      • Mode Density Requirement
    • Achieving Desired Reverberation Times
    • Delay-Filter Design
      • First-Order Delay-Filter Design
    • Tonal Correction Filter
    • FDNs as Digital Waveguide Networks
    • Further Extensions
      • Spatialization of Reverberant Reflections
      • Distribution of Mode Frequencies
      • Reverberation Time vs. Frequency
      • Digital Waveguide Reverberators
      • The Digital Waveguide Mesh for Reverberation
      • Time Varying Reverberators
  • Problems
  • More Problems
  
  
• Time-Varying Delay Effects
  • Variable Delay Lines