Diagonal Complex-Valued State Space Models for System Identification and Modeling of Metal Plate Reverbs
Accurate and interpretable modeling of plate reverbs remains an important challenge in virtual analog modeling of audio effects. While existing neural network-based black-box approaches already achieve high-quality synthesis and strong perceptual quality, they often lack the possibility to identify the underlying physically meaningful complex, long-memory modal behavior. In this work, we address this limitation by proposing a restricted complex-valued diagonal State Space Model (SSM), showing its equivalence to a parallel second-order all-pole filter, also utilizing efficient training via parallel state computation using the parallel scan algorithm. Additionally, we propose a Matrix Pencil (MP) guided eigenvalue initialization, improving synthesis quality and system identification performance.