This paper presented generalizations and new special cases for the matrix used in Feedback Delay Networks. In particular, necessary and sufficient conditions were derived for losslessness of such a matrix. The correspondence between FDNs and Digital Waveguide Networks can be used to obtain FDN parameters based on the physics and geometry of a real acoustic space, rather than by rules of thumb or number-theoretic rules.
In proposing the CFDN structure, we have tried to achieve two goals: efficiency and versatility with respect to the time-frequency behavior. Efficiency is achieved by taking advantage of the circulant structure of the feedback matrix, and it increases with the size of the matrix. Versatility is achieved by introducing the matrix eigenvalues into the design process for artificial reverberators. Passing from the eigenvalues to the matrix coefficients requires only a single inverse DFT or FFT. Eigenvalues act on the distribution of frequency peaks, thus giving controls pertaining to the color and smoothness of the reverberation.
In addition to application of CFDNs in artificial reverberation, we have outlined some other uses as resonators in sound synthesis and processing.