Matrix Filter Representations

This appendix introduces various matrix representations for digital filters, including the important state space formulation. Additionally, elementary system identification based on a matrix description is described.

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Subsections

• Introduction
• General Causal Linear Filter Matrix
• General LTI Filter Matrix
• Cyclic Convolution Matrix
• Inverse Filters
• State Space Realization
  • State Space Filter Realization Example
  
  
• Time Domain Filter Estimation
  • Effect of Measurement Noise
  • Matlab System Identification Example

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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.