Fast Parametric Matrices for Lossless Feedback Delay Networks

Andrea Coppola
DAFx-2026 - Cambridge
This paper presents a framework for designing creative reverbs using parametric orthogonal feedback matrices on Feedback Delay Networks (FDNs) through recursive Kronecker products of 2D rotation and reflection matrices. By parameterizing each 2×2 kernel with a single angle, we construct a family of 2M×2M orthogonal matrices that maintain losslessness while enabling continuous control over network topology. We then exploit their recursive definition to compute the feedback operation with an O(N log₂ N) divide-and-conquer algorithm that matches the Fast Walsh-Hadamard Transform time complexity while offering parametric flexibility. Strategic manipulation of individual kernel angles enables creative sound design applications, such as stereo cross-coupling, selective freeze, and time-varying modulation for resonance breaking.
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