Circulant and elliptic feedback delay networks for artificial reverberation

The feedback delay network (FDN) has been proposed for digital reverberation. The digital waveguide network (DWN) is also proposed with similar advantages. This paper notes that the commonly used FDN with an Ar x N. orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction joining N reflectively terminated branches. Generalizations of FDN's and DWN's are discussed. The general case of a lossless FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDN's 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.