Distributed Modeling in Discrete Time

Julius Smith and Nelson Lee
RealSimple Project¹

Detailed Contents (and Navigation)

• Ideal Vibrating String
• Finite Difference Approximation (FDA)
  • FDA of 1D Wave Equation
  
  
• Traveling-Wave Solution
  • Laplace-Domain Analysis
  • Infinitely long string plucked simultaneously at three points marked `p'
  
  
• Sampled Traveling Waves in a String
• Sampled Traveling Waves in any Digital Waveguide
  • Lossless digital waveguide with observation points at $x=0$ and $x=3X=3cT$
  
  
• Relation of Sampled D'Alembert Traveling Waves to the Finite Difference Approximation
• The Lossy 1D Wave Equation
  • Solution to Lossy 1D Wave Equation
  • Lossy Digital Waveguide
  • Loss Consolidation
  • Frequency-Dependent Losses
  
  
• The Dispersive One-Dimensional Wave Equation
• Effects of Stiffness
  • Digital Simulation of Stiff Strings
  • General Allpass Filters
  • Consolidation of Dispersion
  
  
• Related Links
• About this document ...