There are two common approaches to the design of IIR filters: (a) match the complex frequency response (magnitude-phase) or, equivalently, the impulse response, or (b) minimize only the magnitude error while ignoring the phase response. This research describes a third approach, called magnitude-priority filter design, which merges the two methods. If possible the algorithm matches the complex response, and when not possible it transitions to magnitude only criteria. This is especially useful with quasi-logarithmic frequency-resolution filters because the frequency-dependent windowing of the impulse response requires the high-frequency attenuation to be corrected. Since the magnitude-priority method does not make any assumption about the core design algorithm, this method can be combined with any technique that attempts to match the complex transfer function or impulse response.
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https://aes2.org/publications/elibrary-page/?id=17340
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