Optimal FIR Digital Filter Design

• Norm Minimization
  • Least squares problems
  • Min-Max problems
• Least Squares Optimization
  • PseudoInverse
• FIR Filter Design
  • Linear Phase
  • Complex Filter Design
• Other Applications

References for filter design

• Strum and Kirk
• Oppenheim and Schafer
• Parks and Burrus

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Subsections

• Filter Specifications
• Ideal Lowpass Filter Revisited
• Optimal Least-Squares Filters
• Optimal Chebyshev Filters
• Lp norms
  • Special cases
  • Filter Design using Lp Norms
  
  
• Least-Squares Linear-Phase FIR Filter Design
  • Matrix Formulation: Optimal Design, Cont'd
  • Least Squares Optimization
  • Geometrical Interpretation of Least Squares
  • Matlab Support for Least-Squares FIR Filter Design
  
  
• Chebyshev Optimal Linear Phase filter Design
• More General Real FIR Filters
• Complex FIR Filter Design
  • Related Paper
  
  
• Arbitrary FIR Magnitude and Phase Specification
• Second-Order Cone Problems (SOCP)
• Nonlinear Optimization in Octave

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Next: Filter Specifications

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About the Author: 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.