MUS420 Lecture
Introduction to Physical Signal Models

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)

• Review of Physical Model Formulations
  • Formulation Summaries
  
  
• ODEs
  • Mass-Spring ODE
  • Physical diagram:
  • Mass-Spring-Dashpot ODE
  • Physical diagram:
  
  
• PDEs
• Difference Equations
  (Finite Difference Schemes)
  • Difference Equation for a Force-Driven Mass
  • Replacing Backward-Difference by Forward-Difference
  • Explicit and Implicit Finite Difference Schemes
  • Semi-Implicit Finite Difference Schemes
  • Explicit Finite Difference Schemes as
    Digital Filters
  
  
• State Space Models
  • State-Space History
  • Key Property of State Vector
  • Force-Driven Mass Example
  • Forming Outputs
  • Numerical Integration
  • State Definition
  • State-Space Model of a Force-Driven Mass
  • Force-Driven Mass Reconsidered
  • Force-Driven Mass Reconsidered and Dismissed
  • State Variable Summary
  
  
• Modal Representation
  • Modal Representation, Cont'd
  • State Space to Modal Synthesis
  • State-Space Model Diagonalization Procedure
  • Efficiency of Diagonalized State-Space Models
  
  
• Equivalent Circuits
  • Analog Equivalent Circuits
  • Equivalent Circuit for a Force-Driven Mass
  • Mass-Spring-Wall System
  • Equivalent Circuit for Mass-Spring-Wall
  
  
• Impedance Networks
  • Complex Impedances
  • Important Benefit of Frequency-Domain Impedance
  • Impedance Diagram for Force-Driven Series Mass-Spring
  
  
• Wave Digital Filters
• Lumped Elements versus Distributed Parameters
• Digital Waveguides
  • Digital Waveguide Models
  • Digital Waveguide Definition
  • Digital waveguide model of a rigidly terminated ideal string
  • Digital waveguide model of a single-reed, cylindrical-bore woodwind, such as a clarinet
  • Digital waveguide model for a bowed-string instrument, such as a violin
  
  
• Summary of Models Considered
  • General Modeling Procedure
  
  
• About this document ...