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Description
In active acoustics, controlled feedback is often used to extend a room’s reverberation time by regeneration. This brings an inherent risk of instability, while at stable gains a poorly conditioned feedback system can exhibit quality-limiting colouration. The gain before instability is usually estimated using frequency‑domain eigenvalue measures computed from the open‑loop response, and information about colouration or equalization is sometimes inferred from this. In this paper, we show that while eigenvalue analysis indicates the onset of instability, it does not reliably predict colouration while the system remains stable. We first demonstrate examples where the closed-loop behaviour for stable gains is not predictable by analysing the eigenvalues. We then demonstrate that singular value decomposition (SVD) of the closed-loop operator can be used as a loop-gain-dependent analysis tool. Analysis of simulations and measurements shows a clear correspondence between the characteristics of the SVD analysis and the emerging resonances in the closed-loop response. Furthermore, a spectral selectivity metric is proposed, which indicates the presence of colouration directly from the SVD analysis.