This paper deals with the approximation of a given frequency response by a low-order linear ARMA filter (Auto-Regressive Moving Average). The aim of this work is the audio synthesis, then to improve the perceptual quality, a criterion based on human listening is defined and minimized. Two complementary approaches are proposed here for solving this non-linear and non-convex problem: first, a weighted version of the Iterative Prefiltering, second, an adaptation of the Gauss-Newton method. This algorithm is adapted to guarantee the causality/stability of the obtained filter, and eventually its minimum phase property. The benefit of the new method is illustrated and evaluated.

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