Modal Decomposition of Feedback Delay Networks

• Published in: IEEE transactions on signal processing Vol. 67; no. 20; pp. 5340 - 5351
• Main Authors: Schlecht, Sebastian J., Habets, Emanuel A. P.
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.10.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; artificial reverberation; Decomposition; Delay; Delay lines; Delays; Ehrlich-Aberth iteration; Eigenvalues and eigenfunctions; Explicit knowledge; Feedback; Feedback delay network; IIR filters; Impulse response; Iterative methods; Matrix decomposition; matrix polynomial; modal synthesis; Polynomials; Reverberation; Sound filters; Time-domain analysis; Transfer functions
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2019.2937286

Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. The computational performance is further improved by bounds on the pole location and an approximate iteration step. We demonstrate how explicit knowledge of the FDN's modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that relatively few modes contribute a large portion of impulse response energy.