We show a new sufficient criterion for time-varying digital filter stability: that the matrix norm of the product of state matrices over a certain finite number of time steps is bounded by 1. This extends Laroche’s Criterion 1, which only considered one time step, while hinting at extensions to two time steps. Further extending these results, we also show that there is no intrinsic requirement that filter coefficients be frozen over any time scale, and extend to any dimension a helpful theorem that allows us to avoid explicitly performing eigen- or singular value decompositions in studying the matrix norm. We give a number of case studies on filters known to be time-varying stable, that cannot be proven time-varying stable with the original criterion, where the new criterion succeeds.

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In this paper, we propose a new processor capable of directly changing the microdynamics of an audio signal primarily via a single dedicated user-facing parameter. The novelty of our processor is that it has built into it a measure of relative level, a short-term signal strength measurement which is robust to changes in signal macrodynamics. Consequent dynamic range processing is signal level-independent in its nature, and attempts to directly alter its observed relative level measurements. The inclusion of such a meter within our proposed processor also gives rise to a natural solution to the dynamics matching problem, where we attempt to transfer the microdynamic characteristics of one audio recording to another by means of estimating appropriate settings for the processor. We suggest a means of providing a reasonable initial guess for processor settings, followed by an efficient iterative algorithm to refine upon our estimates. Additionally, we implement the processor as a differentiable recurrent layer and show its effectiveness when wrapped around a gradient descent optimizer within a deep learning framework. Moreover, we illustrate that the proposed processor has more favorable gradient characteristics relative to a conventional dynamic range compressor. Throughout, we consider extensions of the processor, matching algorithm, and differentiable implementation for the multiband case.

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