Computational Acoustic Modeling with Digital Delay

Julius Smith and Nelson Lee

RealSimple Project¹
Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University
Stanford, California 94305

Detailed Contents (and Navigation)

• Delay lines
  • The M-Sample Delay Line
  • Delay Line as a Digital Filter
  • Delay Line in C
  • Ideal Traveling-Wave Simulation
  • Lossy Traveling-Wave Simulator
  • Traveling-Wave Simulation with Frequency-Dependent Losses
  • Dispersive Traveling-Wave Simulation
  
  
• 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
  • Acoustic Energy Density
  
  
• Digital Waveguide
  • Physical Outputs of a Digital Waveguide
  
  
• Tapped Delay Lines (TDL)
  • Example Tapped Delay Line
  
  
• General Causal FIR Filters
• 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
  • Equivalence of Comb Filters to
    Tapped Delay Lines
  
  
• Allpass Filters
  • First-Order Allpass Filter
  • Nested Allpass Filters
  
  
• Feedback Delay Network (FDN)
  • FDN Time Update
  • Relation of FDNs to State-Space Models
  • A Single-Input, Single-Output (SISO) FDN
  • Applications of FDNs
  • Stability of FDNs
  • Stable Feedback Matrices
  
  
• About this document ...