Allpass Feedback Delay Networks

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In the 1960s, Schroeder and Logan introduced delay line-based allpass filters, which are still popular due to their computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we extend the theory of allpass systems to any arbitrary connection of delay lines, namely feedback delay networks (FDNs). We present a characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays. Further, we develop a solution to the completion problem, i.e., given an FDN feedback matrix to determine the remaining gain parameters such that the FDN is allpass. Particularly useful for the completion problem are feedback matrices, which yield a homogeneous decay of all system modes. Finally, we apply the uniallpass characterization to previous FDN designs, namely, Schroeder's series allpass and Gardner's nested allpass for single-input, single-output systems, and, Poletti's unitary reverberator for multi-input, multi-output systems and demonstrate the significant extension of the design space.

Original languageEnglish
Article number9332286
Pages (from-to)1028-1038
Number of pages11
JournalIEEE Transactions on Signal Processing
Publication statusPublished - 21 Jan 2021
MoE publication typeA1 Journal article-refereed


  • Allpass Filter
  • Delay lines
  • Delay State Space
  • Delays
  • Feedback Delay Networks
  • Filter Design
  • Jacobian matrices
  • MIMO
  • MIMO communication
  • SISO
  • Stability criteria
  • Symmetric matrices
  • Transfer functions


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