We propose a new style of continuous-time filter design composed of a cascade of 2nd-order state variable filters (SVFs) and a global feedback path. This family of filters is parameterized by the SVF cutoff frequencies and resonances, as well as the global feedback amount. For the case of two identical SVFs in cascade and a specific value of the SVF resonance, the proposed design reduces to the well-known Moog ladder filter. For another resonance value, it approximates the Octave CAT filter. The resonance parameter can be used to create new filters as well. We study the pole loci and transfer functions of the SVF building block and entire filter. We focus in particular on the effect of the proposed parameterization on important aspects of the filter’s response, including the passband gain and cutoff frequency error. We also present the first in-depth study of the Octave CAT filter circuit.

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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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