Recursive Digital Filter Design

The subject of digital filter design is enormous--much larger than we can hope to address in this book. However, a surprisingly large number of applications can be addressed using small filter sections which are easily designed by hand, as exemplified in Appendix B. This appendix describes some of the ``classic'' methods for IIR filter design based on the bilinear transformation of prototype analog filters, followed by the simple but powerful weighted equation error method for general purpose IIR design. For further information on digital filter design, see the documentation for the Matlab Toolboxes for Signal Processing and Filter Design, and/or [64,68,60,78].

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Subsections

• Lowpass Filter Design
• Butterworth Lowpass Design
  • Butterworth Lowpass Poles and Zeros
  • Example: Second-Order Butterworth Lowpass
  
  
• Bilinear A/D Transformation
  • Bilinear Transformation
  • Frequency Warping
  • Analog Prototype Filter
  • Examples
  
  
• Equation-Error Filter Design
  • Equation Error Formulation
  • Error Weighting and Frequency Warping
  • Stability of Equation Error Designs
  • An FFT-Based Equation-Error Method
  • Prony's Method
  • The Padé-Prony Method

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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.