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Using Resonant Filters for the Synthesis of Time-Varying Sinusoids

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This paper discusses sinusoidal synthesis by means of resonant filters. Resonant recursive filters have long been used to synthesize exponentially damped sinusoids but surprisingly little has been written about stability issues when the filter coefficients are allowed to vary and interpolation problems. In this paper, we discuss some of the issues one faces when synthesizing sinusoids with time-varying coefficients by means of recursive resonant filters. It is shown that different topologies yield different results when the coeffieients are allowed to move, and that stability can indeed be problematic with traditional topologies such as the direct form or the lattice form. Other structure that exhibit good behavior in terms of time-varying stability are shown to perform poorly under linear-interpolation of their coefficients.

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