MUS420 Lecture
Computational Acoustic Modeling with Digital Delay

Julius O. Smith III (jos at ccrma)
Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University

Detailed Contents (and Navigation)

• From Lumped to Distributed Modeling
• Transverse Wave Equation: Ideal String
  • Derivation of Transverse String Wave Equation
  
  
• Traveling-Wave Solution
• Sampled Waves and Lumped Filters
• Delay lines
  • The M-Sample Delay Line
  • Delay Line as a Digital Filter
  • Delay Line in C
  • Delay Line in FAUST
  • Less Predictable Delay Line in FAUST
  
  
• Ideal Traveling-Wave Simulation
• Lossy Traveling-Wave Simulator
• Traveling-Wave Simulation with Frequency-Dependent Losses
• Dispersive Traveling-Wave Simulation
• Recursive Allpass Filters
• Phase Delay and Group Delay
• Acoustic Point Source
  • Inverse Square Law for Acoustics
  
  
• Acoustic Echo
  • Acoustic Echo Simulator
  • STK Program for Digital Echo Simulation
  • General Loss Simulation
  
  
• Air Absorption
  • Acoustic Intensity
  
  
• From 1D$+$ to 1D$\pm$
• Digital Waveguide Models
  • Digital Waveguide Definition
  
  
• Physical Outputs
• Physical Inputs
  • General Case
  • Symmetric Superimposing Outgoing Disturbance
  • Pure Superimposing Input
  • Idealized Inputs and Outputs
  • Amplitude-Determined Superimposing Symmetric Outgoing Disturbance
  
  
• Tapped Delay Lines (TDL)
• Transposed Tapped Delay Line (TTDL)
• Comb Filters
  • Feedforward Comb Filter
  • Gain Range for Feedforward Comb Filter
  • Feed-Forward Comb-Filter Amplitude Response
  • Feedback Comb Filter
  • Simplified Feedback Comb Filter
  • Simplified Feedback Comb Filter, Cont'd
  • Feed-Back Comb-Filter Amplitude Response
  • Inverted-Feed-Back Comb-Filter Amplitude Response
  
  
• Schroeder Allpass Filters
  • First-Order Allpass Filter
  • Nested Allpass Filter Design
  • Nested Allpass Filters
  
  
• Feedback Delay Network (FDN)
• About this document ...