The design of recursive filters with specified magnitude and phase responses is a common problem in audio signal processing. This paper presents a flexible methodology for the design of digital filter cascades with specified magnitude and phase responses based on a non-linear least squares fitting methodology. The proposed methodology utilizes the Levenberg-Marquardt algorithm to derive optimal parameters in the z-plane for a given number of second order recursive filters using a cost function that can accommodate arbitrary frequency-weighting curves in addition to any hard or soft constraints on the filter behavior. The cost function being minimized is based on the L2 distance in the complex frequency domain and incorporates additional terms to impose constraints on filter shape, stability, and distortions.
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