Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation

Davide Rocchesso, Julius O. Smith¹

Abstract:

The feedback delay network (FDN) has been proposed for digital reverberation. Also proposed with similar advantages is the digital waveguide network (DWN). This paper notes that the commonly used FDN with an $N\times N$ orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction and a vector transformer joining $N$ reflectively terminated branches. Generalizations of FDNs and DWNs are discussed. The general case of a losslessness FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDNs using circulant matrices is proposed. These structures can be efficiently implemented and allow control of the time and frequency behavior. Applications of circulant feedback delay networks in audio signal processing are discussed.

Detailed Contents (and Navigation)

• Introduction
  • Prior Work
  • Lossless Reveberator Prototypes
  • Summary and Outline
  
  
• Feedback Delay Networks
• Digital Waveguide Networks
  • Lossless Scattering
  • Normalized Scattering
  • Complexity
  • Conditions for Losslessness
  • Relation of DWNs to FDNs
  • Finite-Wordlength Effects
  
  
• Circulant Feedback Delay Networks
  • Design of Poles and Zeros in CFDNs
  • Computational Complexity
  
  
• Applications
  • Digital Reverberation
  • Physical Room Modeling with FDNs
  • Physical Room Modeling with DWNs
  • Practical FDN Design
  • Resonators
  
  
• Conclusion
• Index
• Bibliography
• About this document ...