In audio, often specialized filter design methods are used that take into account the logarithmic frequency resolution of hearing. A notable side-effect of these quasi-logarithmic frequency design methods is a high-frequency attenuation for non-minimumphase targets due to the frequency-dependent windowing effect of the filter design. This paper presents two approaches for the correction of this high-frequency attenuation, based either on the iterative update of the magnitude, or the iterative update of the phase of the target specification. As a result, the filter follows both magnitude and phase in those frequency regions where it can, while where this is not possible, it focuses on the magnitude. Thus, the new method combines the advantages of traditional complex and magnitude-only filter designs. The algorithms are demonstrated by parallel filter designs, but since the method does not make any assumption on the filter design algorithm used in the iteration, it is equally applicable to other techniques, like standard FIR, IIR, warped FIR, warped IIR, or Kautz filters
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