Series and Parallel Filter Sections

In many situations it is better to implement a digital filter in terms of first- and/or second-order elementary sections, either in series or in parallel. In particular, such an implementation may have numerical advantages. In the time-varying case, it is easier to control fundamental parameters of small sections, such as pole frequencies, by means of coefficient variations.

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Subsections

• Series Second-Order Sections
  • Matlab Example
  
  
• Parallel First and/or Second-Order Sections
  • First-Order Complex Resonators
  • Real Second-Order Sections
  • Implementation of Repeated Poles
  
  
• Formant Filtering Example
• Butterworth Lowpass Filter Example
• Summary of Series/Parallel Filter Sections

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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.