Time Domain Digital Filter Representations

This chapter discusses several time-domain representations for digital filters, including the difference equation, system diagram, and impulse response. Additionally, the convolution representation for LTI filters is derived, and the special case of FIR filters is considered. The transient response, steady-state response, and decay response are examined for FIR and IIR digital filters.

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Subsections

• Difference Equation
• Signal Flow Graph
• Causal Recursive Filters
• Filter Order
• Direct-Form-I Implementation
• Impulse-Response Representation
• Filter Stability
• Impulse Response Example
• Implications of Linear-Time-Invariance
• Convolution Representation
  • Convolution Representation Summary
  
  
• FIR Digital Filters
  • FIR impulse response
  • Convolution Representation of FIR Filters
  • The ``Finite'' in FIR
  • Causal FIR Filters
  • FIR Transfer Function
  • FIR Order
  • FIR Software Implementations
  
  
• Transient and Steady State Response
  • FIR Example
  • IIR Example
  • Transient and Steady-State Signals
  • Decay Response, Initial Conditions Response
  • Complete Response
  
  
• Summary and Conclusions
• Time Domain Representation Problems

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.