Finite-Wordlength Effects

Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation

This class of matrices gives rise to a class of FDNs we call *Circulant
Feedback Delay Networks* (CFDN). The following two facts can be proved
[3]:

*Fact 1*: If a matrix is circulant, it is normal, i.e.,
.

*Fact 2*: If a matrix is circulant and lossless, it is unitary.

It is well known that every circulant matrix is diagonalized by the
Discrete Fourier Transform (DFT) matrix [3]. This implies that the
eigenvalues of can be computed by means of the DFT of the first
row:

where denotes the set of all eigenvalues of , and denotes the set of complex DFT samples obtained from taking the DFT of .

Design of Poles and Zeros in CFDNs

Finite-Wordlength Effects

Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation

``Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation'', by Davide Rocchesso and Julius O. Smith III, preprint of version in

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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